Tribus McIrvine - Energy and Information

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ENRGY AD IFOO The ow of energy in uma soceties s regulaed by  tiny rco of e ngy at s sed for e ow f infrmatin. Enrgy an 1in are also related a a mu deepe level       

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Cii ss Kee s

per"te Ras sai a  cturies ater sciece as in   prase ne eai. Te pr t ic te Rs reerre as pitica ut tat is a sa etai Sciece es t eitate t ie precise e t eryay rs suc as rk" per a irti" a in te prcess t trasr preria truts int scetic truts. Ty e k tat it takes eery t tai kee a tat it taks irti t ars ry. Rarc t te eati tee nery a iratin es ack ay yars ut e era  precise et ena quaticati  iratin an ny it aue E Sas aus 1948 pape Te Mateatica Try  uicati." t as  e k ta ay yaic easurin itruent pace in a t us ra  pr i rr t actuate its eci. Fr eape a ter cec t  ectica circui ue se p t caue te eecti  a pintr Te ect is rciprca ereas te tery  istruetati s y ery is e t tain iratin rece aacs i iati tery s  iatin is ee r trasrati  eey n ti artice e sa purue t ie  tut. eas au y are part  te eucati  eer cientit Sic t ccp  eer is icusse in eti eeer in ti issue e a  rea ta iscussi Te uaentas  iratin try are es  knn We a eree e at e t n  unaeta ias  inrati ere e take up t iter acti  ery an irati eas aut aut praiit praiit a a cenra e in a ter  klee n er irati try praiites are

trte as a uerica eci  a tate  knee s kee aut a partcuar questin ca e rersete y te asie  a certain praity (ete p) t te arius cceiae asers t te questi pete kee aut a questi is te aiity t asi a r praiity (p = ) t a cceiae aers sae e A prn  (crrecty) ais uit priity  = 1) t a prticuar aser iusy as i e t ear aut tat qusti By ri tat kee ca e tus ece i a prity istiuti (a se  praiities asi t te set  piiiies) e can ene iratin as ayi ta caus a ajustet i a praiity assiet Nuerus rkrs ae strate ta San asure  uncertaity c e cae etrpy asurs  uc is epecte  e are aut a questin e a at is k k i  t  praiities ctriutn t e tery anns  iratin as  s e eistece  a easure  iatin ta is epee  te as use  erate te inratn Te inatin ctent  a esae is accri iarian  te r a es t ep n eter te esae is se  ts a aes y ipresi a particuar ape  a carrier ae r y se r  crprapy ce tis inariac s uerst i eces an eieer task t ei g a cuicatis cae n itrui aspec  cuicatin ter is in te seratin ta te rit  a particuar cuicatiscnne esin ies  in  e te actua esae is se u in  e te ce cu ae st a te er esa i i ae en ske t ce A teter ta accuratey nicats nicats 1 ts e c

necte crs a 0t pteti rp s   ay aue  t aays rea 0 ts  ater hat the actu ptt i! Atuh Sas aure  ucertity as ptute r te purpse  esii etter cucatis canes (a as sere airay r ta purps) t as uc raer appicaiity. Ater a ay iece  pyica itruetati ca e iee a a cuicatis yte. Thu a pre (r eape a trcup a prsure trasuc r a eectre) sres as  ser piers ires ias a ecais ere a a cuicatis cae Te uma srr seres as a recer Oe ca appy Sas as t y t te ei  te apparatus ut as t te ce use r cney te irati t is in te atter epec tat te cecti eeen iratin a eery is s itersti Firs e u ee Sa easure Suppe e ae e a quein   a are ucertai  t anser T stateet We ae ee a questi" ees t e ae precse We rquire tat a pssie asrs e nuerate an ta ur c usin e er ic  te pssile asers is te crrec ne.  e ask seti itu ki a te pssie asers are ten e ae  reay pe a qusti e ae istea request p i ruati a qusin n rer t ene Sa easure e ust a it a eee quetin  a a i i a se  pssie aser itu necesari kin ic aner is crrect (Suppse ur queti is Wic uer i tur up  tis ruette ee" T psie aers csit  te nuers n te ruette ee a ur ucertanty arise er ic ur t ct.) 

 © 1971 SCIENTIFIC SCIENTIFIC AMERICAN, AMERICAN, INC

T make thigs mpat e let the smbl X represet ur klege abut  I ur eaple X stas fr all the thigs e k abut the rulette hee iluig ur eperiee it the asi er, the past histr f the heel a the atis f the isreputablelkig pers staig ear the table) This klege, X leas t a assigmet f pbabilities t the aius pssible a sers ssigig p =  t a e a ser is the same as saig, That aser s impssible ssigig p = 1 t a a ser is the same as saig, That aser s ertai less X is f a er speial ature e shall en up assigig iter meiate ues beteen  a 1 t all the pssible resuts ha's measure s repesete sblial b   X t emphasie that the uertait r e trp  epes  bth the ell

ENTROPY IN COMMUNICAIONS was formulated mathematically y Claude E. Shannon in 9 Shannon's entropy S is de· nd in terms of a welldened quetion Q and knowledge   ) about Q In Shannon's fomula the symbol  epeents an arbi tary ale fato, and the sign � means to "um over, r imply add up for eah posible answe to the question Q the prod   the probabiliy  asigned to tha answe and the natural lgarihm of he probability   Shannon went on o de ne the information  in a meage as the dierene between two entropies,  ne taintie: one that is asoiated with knowl edge  before a mesage and te other tha i asoiated wih knowledge   ater a me sage; in mbol,  = SQ   ) - SQ   )

5' - ENROPY IN HERMODYAMICS wa dened by Rudolf lausis in  in terms f a "anfomaion ha lways aom anies  onvesion etwee thermal and ehaial enegy Aoding t asi fomla hen a system hanges frm  tat desribed y  o anthe state desried y  ' the entopy hange S  S i a lated by diiding eah ineen f e ersile he addition Q y th abslute tempeatre   whih the he additio us and addin he oients ve he hange f sat   ste '; the intega io sign syizes his themaia peratin. I a b hown ht Shannons fntin n lasius' fntin ae he s

(fl

ee questi  a the klege

X [see uper iusrion on hs pge J

The athematial eitin f ha nn's etp has the terestig prpe t that if e rretl assigns p  1 t e f the asers a therefre) p   t al the thers,  s  If u k the right aser, u hae  uertait) On the ther ha, if all the prbabilities are equal,  is a maimum If ur i fmati is s sight tht u ust as sig equal prbabilities, u are as u etai as pssible abut the aser) In the preeig isussi e use the klege X abut a questi t e e the etrp  egaig the uer tait f the aser Cersel, e ul hae use  t ee X b saig that a X that maimies   X is a state f maimum igrae abut   ma h es t kn e aser fm ather is as igrat abut  as he a pssibl be The  state f geater igrae s t t k  Hee e a use the ha frma ism t esibe X quatitatiel Other ise X is a qualitatie ept Fr a gie questi  stat) it is f urse pssible t hae ieet states f klege ha ee the i frati i a message i the fllig a  message prdues a e X  e X leas t a e assigmet f prbabilities a thus a e alue f  T btai a measure f the ifrma tin ha ppse that the ifr ati  be ee b the ieree beteen the t uertaities i sm bls,    I X    X' The fratin tet f a essage, the, s a measure f the hage in the bseer's klege frm klege  befe the message t klege X' after the message)  essage that tells u hat u alrea k prues n hage either i kege X reais the same) r i prbabilit assigment a therefre es  ifrmati ha's measure is an enti It as esge t ll a spei nee: t prie a useful measure f hat is transmitte  a mmuiatins han ne t has als bee shn t be the nl futin that satises erta basi re quireets f ifrmati ther I the  eas sie ha put frar his easure thusas f papers hae bee ritten n the subjet a n e as fun a replaement futin, r een a nee fr e O the tar, man a ternatie eriatis hae been fun We lue that the hann entrp measure s funaetal i frati sene, just as te Pthagean thee s funamental  eetr rin

  © 1971 SCIENTIFIC AMERICAN, INC

 ha's ept f etp shul be a useful startig pint fr easig abut frmati presses n general et ha f use hebeenr use befre ha In 1864 Rulf Clausius itrue the ter i his bk Abhdlungen er die me chnsche Weheorie t represet a tasfmati that alas ampa nies a nersi betee theral a mehaial eerg If a phsial sstem hages frm a state esrbe b X a partiular mbiati f pressure, emperature, mpsiti an ageti el, fr eample) t ather state e e b X' a ieret mbiatin f pressure, temperature, mpsiti a magneti el), the arig t the Clausius eitin, the etp hage is aluate b iiig eah iremet f eat aiti b the abslute tem peature at hih the heat aitin  urs a aig the qutets see ower isrion on hs pge J Eept fr the fat that ha's etrp a Clausi us' etrp are repesete b the same smbl a the same ame, there ap pears at rst sight nthig t iiate that the t futis ae i fat the same futi What's i a ae? I the ase f ha 's measue the amig as t a ietal I 196 e f us Tribus) aske han hat he a thught abut hen he ha all re his famus easure han eple M greatest en as hat t all t  thught f alling t ifrati, but the r as er use, s  ee t al t uertait' When  isusse t ith Jhn  Neuman, e ha a bet ter iea Vn Neuman tl me, Yu shul al it etrp, fr t eass I the rst plae u ueraint fu tin has been use in statistial eha s une that ae, s t area has a ae n the se plae, a e mptat, n ne ks hat entrp reall s, s  a ebate u ill aas hae the aatage'  The pit behi  Neua's jest is seus Clausius' eitin f entrp as e lttle iet phsa appeal It a be erie it satisfatr mathe atial igr an a be shn t hae nterestng an useful prpertes, par tiular n egineein, but  a ret aestheti sense t has nt been satis fatr fr eeratns f stuents i ple psial aruents ea ne t be ee in the retness f st quan tties  phss uruning Clausus' entrp thee as alas been an etra ste

The aearane of Shannon's ma sure, wth the same name and the sam untonal esentaton as th earle easure n statstal therodnamis, aoused great nterst among theortial hssts One of the bestknown ontibutos to the subsquent disussion was Lon Blloun, who teated the two entroies as the same in a sers of paes and n the book Science d nfo mion Theoy The oof that the are nded the same (and not mere analogues has ben deat wth xtensvl elsewhere an wl not be treated here





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of inforation s detrmined heb unit th hoie of the abitrar sae fator K in Shannon's nto fomua If K s made qual to the atio /ln 2 (where th exression n 2 rsnts the natura" loarithm of 2 thn S is said to be measured in bits" of nfoma ion  ommon themodnmi oie or K s k where  is the nuber of moeuls n the sstem onsded and  s 138 X 10- oule  dere Kelvn, a quantt kown as Boltmanns on stant Wth that hoie for K the entro of statstal mehans is x pssed n unts of oules e dgre The smlest themodnami sstm to wh w an al Shannons qua ton s a singe moeue that has an qual robabt of bng in ethr of two stats, for xaml an lmntar agnet In this ase both  and  equal 1/2, and hee S quals +k n 2 Th emoval of that uh unertaint oresonds to one bit of nfomtio Tefoe a bit is equal to k n 2, or ap oximatel 10- oule e dgre K Tis is an motant gure, the salest thrmodami en hange that an b assoiatd wih a masuement ied ng  bt of nrmaion In lassi thmodams t has long ben kown tat te nto o mixing, r moua weit of mix tu, is a funion of th fationa om osition bvious the frational on ntration of a prtiua molua se es presnts the robabilt of ik ng out a oeule of that ses in a ando samng of the mixture What os the at of ixing signif f we use the no of xing as a masue of nfomaion? Imagine that we mix haf a oeua wigt of eah of two sotoes The esuting nto hange woud be ok n 2, where o (vogados numb, 6  10) s the nume o molues  oeua wigt Nurial tis hane is about six oues r dge K, or 6 X 10 bis  t t numbr rrsns t numbe of

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AXWLLS ON, a hypohel beg oked by Jame lek xwell    a poble oator o the eod law o hemodm, wa umed o opere a mll rp doo eparag two veel ull o ar a a urm emperure t By opeg ad log the tapdoor o a to allow oly he we moleule o p rom  to B d oly the lowe oe to p om B o  he demo ould, whou expedtue o ork, e the tempeure o B ad lower th o  tt  odon to the eod lw o thermodyam. he demon w lly "exoed i 9 by eon Brillou, who poed out h  he demon were to dey he moleule, he wold have to illume hem  ome way, uig a ee  epy ha would more hn ompete r ay dereae n eropy uh a beg ould ee Whout he pu  eergy repreeted by the illumnao, he demo lk ue mo o he he eergy  the moleule

  © 1971 SCIENTIFIC AMERICAN, INC

esons ha would have o be made f a peson wee to sor he sotopes one at a me Just as he eno of nformaon has eanng onl n relaton o a welldene queston so the enrop of her odnam analss has meanng onl n relaon to a welldened ssem In our presen understandng of phsa sene ha sstem s ene b quan um heor The queston s: In wha quantum state s ths sstem" The an swer s In some satstal ombnaton of sates dene b he quanume hanal soluons of the wave equaton" n fat these solutons dene he poss bltes we alluded to n sussng nforaton an unerant The pob abltes enoe our knowledge abou he oupan of the possble quanum saes (possble that s for a gven state of knowledge) of an nherent onne  eononet beween he enrop of Clausus and he ntuve noon of nformaton preeded Shannon's work b man ears n fa he nformatontheo aroah o hermonams s almost as old as hermodnams tself Clausus' 864 ook eresents he earles omlete ormulaon of lassal (nonsatstal) hermonams B 8 James Clerk

Maxwell ha nodued the role of n formaon b poposng h faous de mon see Maxwell Demon" b W Ehrenbeg; CIII IC No vembe 967] He suggesed hat a demon of mnue sze ough o be able o oerae a small rapdoor saratng wo vessels permng fas moleuls to move n one reon and slow ones n he other hereb reang a derene n emeature an pressure between the two vessels [see iustrtion on pe ceding pge] Maxwell's emon beame an nelltual thon n the sde of thermod namsts fo almos a entur The hal enge to he seond law of hemod nams was hs: Is he prnle of the nrease of entrop n all sontaneous proesses nvald where ntllgene nervenes Fro Maxwell's me on man leadpondered the rlaton ng beween observaton and nformaton on he one han and he seond law of hermodnas on he other For ex amle n 9 J D Van der Waals speulated on he elaton between en ro hange and he proess of rasonng fom ause o ee In 99 Leo Szlard ommened on he ntmate onneton between enrop hange and nformaon In 9  N Lews wrote: an n entop means loss of nfor

aon; othng more" Untl Shannon ame on the sene however here was no measure of nformaton so that the dsussons ould not be quanttatve What Shannon added was the reog nton hat nformaton tslf ould be gven a numeral masure If an of the earl hrmodnamsts had hosn to do so he ould have dnd nforma on to be onsstent wth thermodnam ento ft all the enro of mxng" was wll known n one of hose mn ould have hosn to dne nformaton as the number of dsons requrd to unsort" a mxtur The Shannon masure would hav followed Shannon who had no diret ntrst n thermodnams ndndntl develoed a masur of nformaton For ratal rasons he hose to requre the measure to t rtan logal rtera of onsstn and addtvt In rtro set a logan an how that wth hese rtera Shannon was bound to ro due a measure that would b onssten wth thermodnam entro On t s eognzed that the two subets de ve from ommon onsdratons t s straghtfowad o dve one from the oher The Shannon formulaton s somewha more gneral sne t s entrel a mathematal heor and s alable

ENRGY (JOULES)

INORMATION CONTEN (BITS)

ENERG PR INFORMATION (JOULES PER BIT)

 TYPE ONE PAGE (ELETRI TYPEWRITER)

30.000

21000

1

 TEEOPY ONE PAGE (TELEPHONE FASIMLE)

20000

21.000

5400

21000

3

500

21000

07

120.000

22,400

 TRANSM T 3000 HARAERS OF DATA

14000

21000

7

READ ONE AGE OMUER OUUT (ENERGY OF LLUMNATION)

13000

50,400

3

SORT 3,000-ENRY BNARY FE (OMPUTER SYSEM)

2000

31000

06

PRNT ONE AGE OF OMUTER OUPUT (60 NES x 120 HARAERS)

500

50400

.03

ACTIVIY

CHARATER REORD ATIVITIES:

READ ONE PAGE (ENERGY OF ILLUMNATON) OPY ONE PAGE (XEROGRAPH OPY) DGTAL REORD AVTIES: KEYUN 40 OLLERITH ARDS

RAIOS OF ENERGY O INFORMAON or various inoma tion-preparation inormationproessing and inormationdistribu tion ativities involing symbols are presented in this table he energy values used are those typially involved in poering the mehanisms employed or these ativities and in most ases are

5

aurate only to about an order o magnitude For harater reords inormaton ontent is assumed to be about seven "bits pe ara ter he energy/inormation ratio or inomation systems based on harater eords and digitally enoded eords varies rom a e joules per bit don to a e hundredths o a joule per bit

  © 1971 SCIENTIFIC AMERICAN, INC

to all kinds of nertaint. The thermo dnami theor is less general sine it is bond to or real wold" environment of atoms, moleules and energ. Bril oin tried to emhasie this distintion  seaking of fee information" for the stra Shannon qantit and bond information" for the qantit when it desibed hsiall eal sitations (and ths themodnamis s we shall see in onsideing ratial informationroessing ativities, the onl real distin tion is that natral hsial sitations in volve mh larger amonts of information than we aear able to ontrol in or hmanoriented information sstems. There is no onit between abstrat Shannon information and thermodnami information, as long as the qestions we ask are hsiall eal qestions interesting aliation of informa An tion theor to themodnamis is

rvided b rilins exorising" of axwels demon. s we mentioned aove, the demon ed to aarent ther modnami aradoxes. Brilloin ointed ot that if the demon were to see the moleles, he wold have to illminate them in some seial wa. Sine the blakbod adiation in a gas vessel is the same in all diretions, withot a toh the demon wold have no wa of distinguishing the loation of individa gas moleules. It takes seial infomation to harness the eneg of the moleules, and this infomation is above and beond the norma themodnami infomation that serves to distingish the sstem itself from its srodings. Without the deartre from eqilibrim reeseted  the torh, Maxwells demon aks the information on whih to at. Unlike the demon, we o not ive inside a gas vessel in eqilibrim at a niform temerate. Sose for a mo ment that we did. Imagine that the earth is ontained in a totall absorbing lak box" at a niform temerate of 90 degrees K. (6 degees Fahrenheit, a easonale estimate of the eal earths average sfae temeratre. We wold e as heless as Maxwells demon withot a toh. In site of the large energ x and the modeate averae srfae temeratre, an earth at eqilibrim in an ambient envionment wold be inhositabe to ife. No information ould be oessed; no eneg would be avaible in the themodnami sense. The atal ase is of ourse dierent The eath is at of a snearthsae" sstem that s qite ot of eqilibrim. The sun las the same ole fo us that the toh did for Maxwells demon. B oviding a deatre fom equilibim

it beomes a soe o information and sefl eneg. In onsidering the man se of en eg and information, we mst ake into aont the adiation balane of the earths surfae. The eah eeives 16 X 105 megawatthors of energ fom the sn eah ear in the fom of sola eletro magneti radiation, and it eradiates this energ iniall as blakbod adia tion. Ths the eart aroximatel balanes its eneg dget. Mans se of en erg on the earths surfae atall on stittes internal transations with eneg uxes that are thermodnamal avail able, that is, usale before the eneg is thermall degaded to the aveage sfae temeatre or hemiall degraded b dision to the environment. Taking ommonl aeted average values fo the temeatres of the sn and the earth, the 16 X 105 meawatthos of energ adiated to oute sae aries with it the aabiit fo an ento derease, o negento x," of 3 X 10 joles e degee K e ear, o 10 its e seond. Of ourse, this negentro ux derive fom the energ x fom the sn to the eath to dee sae. B stoing the ener g and negentro in vaios sstems (fossi fuels, akes, lods, green lants and so forth, the eath eates subss tems that ae ot of eqilibrim with the general envionment. In addition to the solar ux, then, we have the stoed energ and negentro of the eaths esore. Onl in the ase of the otential se of deteium in fusion reatos does this stored energ exist in amounts signiantl greate than one ears solaenerg ux. Fo atial uoses we ma onsider that both the energ ux and the negentro x at the eaths srfae are de to sola roesses. On the srfae of the earth, therefore, the maximm steadstate ate at whih infomtion an be sed to aet hsial roesses is of the order of 10 bits e seond.  great deal of his information is sed" n meteoologial roesses (lod fomation, thnderstorms, the es tablishment of highaltitude lake and watesheds and so on).  arge additional amont is sed" fo the ife resses of lants and animals.  omarativel small qantit is nde the ontol of man, et this quantit is esonsile fo mans tehnologial eshaing of his envionment. The limitation of 10 its e seond is not a stringent one. Conside the info mation ate of a television broadast Television stations boadast 30 fames er seond, eah frame ontaining  sa lines. The esoltion along eah

san line allows abot 630 bits of information to be enoded. The eslting information ate is 30 X  X 630, or 07 bits er seond. Suose e now onsider a totall nonredndant television boadast one in whih eah dot is n orrelated with the othe dots on the same frame and eah frame is nrelated to other frames. No hman being old ibl absob information from a television tbe at sh a rate. Even if the material being broadast were a tial inted ae (and on sh a age there is a great del of orrelation between dots it wold take a erson of resonable skills abot 60 seonds to absob the inormation fom one frame. Ths e an estimate the robable bit rate reqired to engae a hman being in inteletl ttention as being less than 104 bits er seond. With a world oulation of less thn ve billion, the entire hman ae old have its information hannels individal sevied nd satated with a bit rate of  X 10, ve mh less than the 10 bits e seond available an old mxims oint ot that talk is  heaer than ation.  omrison of the entro balane and the eneg balane on the srfae of the erth indi ates that the maxims are indeed a reetion of or exeriene. The amliation of information is esie than the amlation of ower. The total msleowe ott of the hman ae is estimated to be abot 3 X 10 megawatthors er ea (somewhat less than one megawatthor e erson e ear. orldwide ower sge nder hman diretion is of the order of 7 X 10 megawatthors r ear, so that the eergamliation ratio r entl is abot  to one. In the . the amliation is mh larger: roxi matel 0 to one. If all the therod namiall available solar energ were sed, an amliation of 0000 to one is theoretiall ossible. The ossible amliation of inform tionroessing ativities is mh greater. B eliminating the hman oerator from the hain of dataroessg d mahine ontrol over hsial sstems, an diet deendene on the ntral te of human datahandling is removed.  human oerato, working with a xe set of qestions, an se a mode digitl omte to amlif his bilities b a fator well in exess of 10, erhas  a fator of 10. The weak limitation on in formationroessing rtes de to adi ation to sae (10 bits er seond) wold indiate the theoretial mximm amliation to be in exess of 10"4

M

  © 1971 SCIENTIFIC AMERICAN, INC

 s rt servng a is gea ga eeen e aceve a he cevale gives fran eclgy  charace ere  a f atels ecnlgy  energy eclgy  aeals ecnlgy n energy eclgy scentss e accuste  suyng funaenta ltains an ual suctures an engneers ae acuse  esgng in a fe rers f agntue f ese ltatins n fran ecnlgy scientists n unaental eres  a all restic ve, an erepeneurs scver ta he ree fr cnsrans akes ssile e cstructn f an als ttally ne envnen f nfatn Hence e ven f elevisn prgraing, aut tic elepne slicat, cputergenerae junk al an he aifacts of an nfrai vela" culue n e case f aerial an energy atue ofen cres Hal!"  he chages rught y ecngy n e case f infrain a hself ust ssue te rectves  ensure ha teclgy s se  huan eteen nte Brlluis exrcsg We have Maxell's en Begining it s ac Brilluin as le t vestigate e elan eeen te entrpy o an observati a te theyamc enr, a e ccue tha e i f mn equres  In 2 erl en

y uts s Denns Gar e put it: Yu cn ge seting r nhig, n even an servain" Tis cen as a special eg fr tse f us  ae egage i the esig f xergrac cpyg euip en ng ter reass fr ccen bu nfrat an energy prcesses, e are nteeste n he ium eergy eureen fr akig  cp Te ac ual eergy use a present is cveniely ig (ainly ecause te xing f e al image akes abut 90 percet  te e an vlves therall fusig e blck ner t e paper,  s we sall n iscuss e subject futer We scvere, heve, that readig ur cies ften takes uc re eegy an aking te ( tpcal edg re uireet igh e 5,400 jules fm  90secn esue  a 60tt la Jus as Maxell's den culd t see lecules ithut a tch, s e a see ages ithut llumat me uus ux mus be eset vig electrmgetc radat m a tem peratue geater ta h f he evrn et I he pcess f themaly de gradg that eegy a sgal s geerated The istrbutin f reectivity ver the suace f the paper dutes te negetpy ux m the llumt Bth he paer ad he illumatr are equired fr te etrieval f imat  far e ave ccetate n te

frmt neee t hress enegy N t is te t exaie he pactc sects  e energy euireens f ifrtn syses The rl f nfti techlg cludes b gt ad algue epesentatns an  uses e ae f the The aa s f he utlit f igital cmpuers setimes leads us t verlk te e m eresetatis f ifn  ges ad aud sgals Fr all e secies  irmati representatn  ca sder e fllig distngus able actvtes the peparatin f recs, the stage  recrs, te prcessg  recrs a e istrbut f ecrds Imtin stage s a assve acivity,  t es nt trsically reue the ctiuus pu f eergy athugh n fact sme fms f stage, such s a semicductg dgtalc puter mmy, d have e euiremets Imati pepatn, ifrt pcessg d atn dstbut all equre eegy he ale n pge 12 lsts the mati cte ad the eegy i certa pactical eupme cguats used  a nue  ctivites ivlvg chaacter recs ad digtally encded chaacter recds ice the chaacters are chsen fm a lmte set, the fmat ctet s but seven bts per characer ( the cse  n dgital chractes e eglec

EERGY (UE)

RA T CTET (BT)

O OVSAO (O MU)

2,0

2.000

00

G FY AUO ROD AYAK (O MU)

3.00

200,00

00

600

,20000

0005

0.00

56,00

03

3000

.000.00

02

50

000,00

00

0.00

50000,00

0002



300.00

ACTIVITY

EERGY PER IRATN (UE PE BIT)

AUO O AVS

AM AO ROAAS (O MU) OA OD AVS: OY O AG (O FASM) POJO OF 35 MM S (O MU) OY O AG (XOGRA OY)  O G QUAY OAQU OOGA PR (5" x 7") ROJ O VSO FAM (/30 SOD

E ENE/NFMAIN AIS generay exit f nfrmatn atvtie nvving aud and tria epreenta n i tabe vertate nfrmatn ntent ne te fu band idt f avaiabe feqene  never ue i audi atvtie and e typia ta er ntain a great ea f edundany.   eut t eergy / nfrmati vaue are  mt ae aurate

0000

 e tan an rder f magntude, but tey are uggetive t  ear, f exampe, that the inrmatn ytem tat ue te mae aunt f energy er unit nfrmatn i a ytetia nnredu dant teevin bradat Even ti maativey een inf matin ytem ue fr te urpe f mmunatin n a tn fratin f te termdnai infrmatin t requie t erate

  © 1971 SCIENTIFIC AMERICAN, INC

e possibility of added ifoatio  e for of ages of fot, boldfae, talis ad ote additos to sets of ar aters e eeg is te eergy volved i poerig the eaiss typially eplyed i ese ativities ad  lluiaig pages for readig Mos of the values are auate o iti about a order of agiude I e table e alulaed the illuiao fro a 60 at lap Obviousy oe a also read uder a highpoer ar lap or by the ligh o a adle he eerg per ortio ui paly varies ro a e oues per bi do  a e hudeds o a oule er bi iilar ioatio is oaied i he be o age  or pratal equpet oguraios use i aiviies i volvig audo represeaios ad pitorialage represeaos We have used tpial values or slideproeor l luiaio, radio ad televiso reeiver poer ad telephoe etraloe po er Clearly he values vary i iividual isaes Addioal ueraties arse fro our estiates of iorao oet Audioitesity odulaio, pitoral gray sale ad olor ositute ultilevel odig teiques For ultilevel odig te iforaio aaiy of a ael is relaed to the sigalooise

ararisis as ell s o he freque adidth Fro a pratial poi of vie hoeve, te ale overstaes  forao ote; he ul badidh is ever used i audio ativiies ad e typial ioial reord has a geat deal o reduda he values are hu aurae o less ha a order o agi ude, but tey are oeheess sugges ive A exee ase of reduda at teds a 3illieer pitorial iage of a page of pit Assug a resoluto o 00 lie pais per illieter, about o ilio bits are used to represet appoxiately 3,000 haraers Most o he ioraio s reduda ad is used to ovey te ite spaes, he detals of e arae fot ad oter aeria a ay e of o portae to the es sage Eve a fouleter ord ould tae up a llio its  a ghresolui pho torap At te other extree a siple, oedudat olevel audo od a be used to represet he sae our lette ord  oly 2 bits tehology has as oe of foaio its prese oers e est use of

eergy ad pysial srutures to o ve iforato as eeded for ua puposes, tou udue reduday

E + PoV To

 � j Nj

E + Po   To S To

L � j  j

HREE EQUAIONS show the derivation of the onept of therodynai inoration he top equaton s based on assia therodynas: So is the nertainty when energy ( ), voue  V  and the nube of oes of various heia speies (N) are unreogni able beause they are distributed in an environent at a tepeature o  a pressure o and hea potentias f o  he idde equaton s deived fro the top one on the basis of the reation  = So  S here  is inforation and S is the unertanty about the syste fored with energy  voue V and oposition Nj and the syste is now disernible fro the environent hese equatons ere derved by Robert B Evans, now at the er gia Institute of ehnoogy, in 99 He shoed that a new quantity obtained by utipyng the idde equation by  is the ost genera easure of disequiibriu or potentia ork Evans has naed this new quantity "essegy (for the essentia aspet of energy ) 

   © 1971 SCIENTIFIC AMERICAN, INC

ad yet ih veraity, style ad as As a part of tat oe te oit poesses of eergy o ad ioratio o are of speial iterest e are led a to te osideratio of he eodyai fuis of a physal sys te hat is ivolved i iforatio proessig I he disussio hat follos e shall ae use o deas reetly developed by Robert  Evas, o at e eorgia Isiute o eholo, ho has devoed a deade  e uraveli o he uesio he oraioheory treae of heodyais aries he oept o equilibru A e oes thougt shoud serve o ove oe hat the oepts isiuishable ro the evroe ad Out of equilibriu are the sae Our abiliy to reoge a syse depeds  the a tha it dies fro its eviroet herodyai orao is oeptualy he sae as egree o deparure o equilibi u I eah o hese quatites is ea sured i su a ay as to satisy te ee eary propertes of additivty, osisey ad ootoi rease i te systes sie, te apar fro us o easure ea ill e the sae atheaial expressio, sie thy really re fe to he sae ti erdyai foratio s de ed as e dieree etee o e ropies:  =     reers to the etropy of a syste of give eegy, olue ad opositio  s the eropy of e ae syse of eegy, volu a o positio e t is iused ito (ids tiguisable  a refereed evroet I easures te loss o iora o  ot beig ale to disiuis te syse fo ts suroudigs (as he a eerg elts i he ope sea e idea of usi therodyai iforatio as a geeralie easure of he availaility o eergy as rst pu forad tetatively y Evas  1965 (Alouh eat eergy, ehaial eery ad eial eegy a be oeted  oe aohe, tey ae ot equally available to do or Wha  all aot eiey ad is ree eery ere veted o deal it e availability of eery y 1969 Evas subied his dotoral dissertatio otaig a etirey lassial poo at a e quatiy, obtaie y ultiplyi is forula or herodyai ifoaio y a appropriae eferee e peatur, has ost uusual pperties vas has alled tis e fuo essergy, or he esseia aspet of eergy [ee iusro  ef He has deo strated hat essery is a uique easure o poeial or Moreover, i ior

The ging power mn: i futu lads pull  pl u? Evey year, the U .S  adds more generating capacty to ts el ectrcal systems than does all the rest of the free world And t's stll not enough  Helpng Amerca's utl tes meet the g rowng n eed for more power s bg busness for Colt In dustres Today were better tan ever prepared to help, through o r nw letrc Utlt Sales Dvso, fomed to oer the nd ustry essental equ pment and systems from a un fed so rce Among the produs we sup ply are Central Moloey power ad srbuton trasormers    ragng from gants andl ng hun dreds o ousas of kowas to m -n ts oy   nhes

hgh   and hghvoltage power crcut breakers to safegua rd costly trans msson systems Hund reds of m les of welded stan less steel tub ng fro m our Tret be Dvson go nto powerhouse condensers and heat exhangers O r desel ge erators are used for base loa a d peakng power generaton and nulear power lant proecton An you'l  nd ou r Farbanks Morse pum ps a Q ny compressors, too  even sysems to wegh the m l l ons of tons of coal consu med by tl tes Helpng keep Amera growng has been our a m ever snce Sam Colt massprouced the poneerng revolver

that tamed t he West Our   dvsons and ther   plants serve not only electrc utl tes ut vrtual l every other n dustry   aomotve, aerospace and transportaton, chemca and petrochemcal, constructon, securty and defense, agrclt ure and food processng  Over $665mll on n sales l ast year A sonofag n of a c ompan y Col Ind ustres,  Park Avenue New Yor, New York  Yo rem ember us e tame frontes

@

COh Induries 87

 © 1971 SCIENTIFIC AMERICAN, INC

•  \

\1 ,

r buddi asryscs ad bacyard asrr

Atoms Stars and Nebae risd Lwene lle

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p  c   pvuy  mu f ptu fm u u (uch  Gbb f gy Hmtz f gy th fuc ud  Gmy u th m  gy" t K vby fuc  d   O c  t f tmdymc fmt   f m utty ptg th g  t" f  ym    vmt T Rc tht  0  th th m gy p g f frm d tht v g  T h   f t r f T     g th fmt pcg Wh   g   dg    p F mp  t u f ctmgtc gy h u f  gy  ut t b th m  ht  c t Pyg vctr C t   t th u f gy  g ugh t c  m; f y t b cm  k g Ev rgy fuct  pv ufu  yzg p cyc p cury f cmc ptmzt Af   gy c b thr ct r ry  tht  rgy bc fr  tm p p   vy  ghtg A rgy bc hvr b  t trc  pc p cc   h thy ct kg  h th  a h th  gy u f 6 X 1 mg tthur p y u b u f t rt t u pc r  ccmp by  tpy u f 3 X 1 ju  g  (Th crr g chg  gy  6 X 1 gthu p yr y a gy y cu b prfm  th aur pc f th th' ufc Th u frm a fut fr cgcy u pg f  rgy utzt by m c  u v  ct f t tubc cu by pp gc chg Th ufu f th gy fuc  rctc mtt h y b mt   cmptv y f th f mkig frh tr fm tr   gz tuy f  pt f  tu t th mp f fr tym ctvt t  th t b  pg 2 d  t   p b t cmp rgy  frt u y cmprg t crbut t gy chg Th p th u   ut f rgy p u at  h ut t  acat th  bt f  rat a a ct f  ju Y h frt chg p a ctr u f y 1 X 1 ju f r g   r f gy ru

 88  © 1971 SCIENTIFIC AMERICAN, INC

mt th fmtcg pc f  tv bct   ght Wt   mty g h th  gy  ht th m A m   d h tht ch mp f ht  hv c  fmty tm cvty   fct  gy ctvty tht c th t  m mut f  fmt Nt ut fmt ch gy rch th tt f hg  fmt t  bt p mcu    dg  frmt pc  th thmymc  Php t  th  gp bt th mut f ty tht  mu  pcc fmt ytm  h tpy f pyc ytm tht h  t  ruc tc  th p f cic thmy ct t dpt th frmth ry vw f th fut f thm dymc  b  cd c th ppr  t c f th t ttbk t v tmymc  th b f fm  thy Th trv h t   cv fm t cc trt T cc trtmt m mr  trch h vr  jug fr  ct cfrc f tch f thr ymc   f h vr crg mptc f fmt tchgy  t ctc  h  uftut Prhp th    th cmmt f th Ru rk A  Vk h rt  11 prp f h  t tp t tuctur thmymc Th rt pt [t th] brch f phc  u t htc r thr th t t tur f t ubjct ttr A gca vpmt f cc mu  vtby t th u ct f th   uch  uc t h t y cm but y b cu th ctuy trt utr trppg g th u f th c c cc thmdymc hv b f th prcur z Ap prty  rg p f th f h b b  th uthy f h g u h bugh th u f c c  tc" Whtv th hrt utcm  ucat cc   ct ht th ccptu cc t fr t  h c a f thrm ymc   y tbh T u f bu fmt"  th  u  f c v gy Th u f rgy   c  f thrya avbty  cty v at Tu  frt a gy a ca tv  a   h  f th bva Scientia p tesas est.

To each i/own. Not everybod needs a concer gran piao, nor does everyody need the et ctdge Shure mkes to enjoy s knd of muc on h knd o h- syte. Eventuly, you'l wnt the renowned - Type " Improved, the ples cartrge for adnced system  and ampe udgts. But, f yo xhequer   lttle tght coder the M wdey accmed as te ec be ctde n the word Wth a sharp crcum ce udet a s tar from ost. Chooe any of the four modes  the M44  e r  , ut for optmum erformance In te eas-ak $18-25 prce rnge Wrte for a comete catg: Shure Brothes nc., 22 Hrty Ave Evanton nois 6004.   © 1971 SCIENTIFIC AMERICAN, INC

What's the foreca st for Aegeny Ludlum Indusries ? hats the forecast for power The explosive dmand for electr power has a whole i ndustry nnng j ust to keep up . And when the poe people moe,  do we. Beca use our Walinford St l produs stainlss condnsr tubs or nucar powr plants stainlss stri or many aiations indin a nw ndrround ab wrap Spi Mtas mas sophistiat ih tmperatur aloys or trbine componnts and nuar rtors. heny Lulm Stl producs rain-orinted siicon sts for nerators and trnsormrs ctria aoys for motor  ontrol reostats a n a host of otr trial spiatis rnold Eninerin contributes with Sictron cores or distribution and power transormrs nd tose are j ust te hih spots Whn tomorrow happens we'll b th r waitin or it in al the iht place Lie the power marke. Wating with a tihtlynt group of companies all ith interrelate technooies and all rowth oriented Wats the forecast fo Alegheny Ludlum Industres? Wee got our wok cut out fo  . . . moe power to you. Aleheny Lulum Industries Inc. Dep t. B-4 Olive Bldg. Pittsburh Pa  5 2 2 2

M INDUSIE TOMORROW IS. 1 90  © 1971 SCIENTIFIC AMERICAN, INC

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