124 Maxwell's Demon t iOIl men \dl('~ ing Ii hy d A kllO\' "pel' chill "au ON THE DECREASE OF ENTROPY IN A THERMODYNAMIC SYSTEM wol'l BY THE INTERVENTION OF INTELLIGENT BEINGS trill fiuct! LEO SZILARD wou long' t 11(' WOl' nonl pl'n. play Wlll the Translated by Anatol Rapoport and Mechthilde Knoller from the original article "Uber die Entropievel'. 01' II Zeit~chrift mindenmg in einem thermodynamischen System bei Eingriffw intelligenter Wesen." /111' whe Physik, 1929, 53, 840-856. fol'll entropy in connection with the lIleasure· call The objective of the investigation is to ment, therefore, need not be greater than esta find the conditions which apparently allow Equation (1) requires. onl the construction of a perpetual-motion ma­ whf:' chine of the second kind, if one permits an tem HERE is an objection, already historiCILI, tive intelligent being to intervene in a thermo­ against the universal validity of tim veil dynamic system. When such beings make TSecond Law of Thermodynamics, which ill­ 81 measurements, they make the system behave deed looks rather ominous. The ohjectioll 1M fal' in a manner distinctly different from the way embodied in the notion of :\Iaxwell's dcnlllll, pcrl a mechanical system behaves when left to who in a different form appear... en'n nowlL chi! itself. We show that it is a sort of a memory days again and again; perhaps not umCRHOIl hut faculty, manifested by a system where reg measurements occur, that might cause a ably, inasmuch as behind tilt' prcciHllIy intl' permanent decrease of entropy and thus a formulated question quantitative <,Olnll'C' A violation of the Second Law of Thermody­ tions seem to be hidden which to date IIIL\'" pos namics, were it not for the fact that the not been clarified. The objection in itH odIC' of p measurements themselves are necessarily nal formulation concerns a tIl'IIIOII who as a accompanied by a production of entropy. At catches the fast molecules and lets till' ,dolY t.im first we calculate this production of entropy ones pass. To be sure, the objt:-ction mil hI! ing quite generally from the postulate that full met with the reply that man cnnlLot in pdll inte compensation is made in the sense of the ciple foresee the value of a thel'lllully 'hit' Itt R Second Law (Equation [1]). Second, by tuating parameter. However, onc' ('ILIlIIO! Thl\ using an inanimate device able to make deny that we can very well ml'Ul'lllrCl lit" measurements-however under continual value of such a fluctuating pal'UIIH'lm' I\llll entropy production-we shall calculate the therefore could certainly gain ellf'rl/;~' ILl. thI! resulting quantity of entropy. We find that expense of heat by arranging (Jill' illt (,I'Vt'l' it is exactly as great as is neees;;ary for full compensation. The actual production of l1P I L Szilard 125 tion a('('())'{lil1g to til<' re"nlts of the measure­ as well as the motor nel'Vous systems a l11<'nt::;. I're"ently, of ("ourse, we do !lot know degradation of energy is always involved, whether \\'e ('omJllit an elTor by 1101. includ­ quite apart from the fact that the very ing tlw ilJterYening man into the system and existence of a nervous system is depC'ndent by di"regarding his biological phenomena. on continual dissipation of ellergy. Apart from this ulll'esolved matter, it is Whether--considering these circum- kno\\'11 toda~' that in a system left to itself no stances-'real living bC'ings could continually "perpetuUlIl mobile" (perpetual motion ma­ or at least regularly produce energy at the chiJl(') of tIlt' second kind (more exactly, no expense of heat of the lowest temperature ap­ rEM "automatic machine of continual finite pears very donbtful, even though our ignor­ \\'ork-yi<'ld which uses heat at the lowest ance of the biological phenomena does not temperatuJ'(''') can op<,rate in spite of the allow a definite answer. HowC'ver, the latte!' fluctuatioll phenomena. A perpetuum mobile questions lead beyond the scope of physics \\'ould haw to be a machine which in the in the strict sense. long nlll could lift a weight at the expense of II. appears that the ignorance of the bio­ tIl(' lH'at content of a reservoir. In other logical phenomena need not prevent us from words, if \\"l' want to use the fluctuation phe­ understanding that whieh seems to us to be nomella in order to gain energy at the ex­ the essential thing. We may be sure that pem;p of Iwat, we are in the samc position as intelligent living beings-insofar as we are playing a game of chance, in which we may dealing with their intervention in a ther­ win celtain amounts no\\' and then, although modynamic system-can be replaced by non­ the expcetation value of the winnings is zero living devices whose "biological phenomena" ler­ or !legative. The same applies to a system one could follow and determine whethm' in fIll' when> th£> intervention from outside is per­ fact a compensation of the entropy decrease formed st riel ly periodically, say by periodi­ takes plaee as a result of the intervention by eally moving machines. We consider I. his as such a device in a system. established (Szilard, 1923) and intend here In the first place, we wish to learn what only to ('onsider the difficulties that occur circumstance conditions the decrease of \\'hen illtelligent being'S intervene in a sys­ entropy which takes place when intelligent tem. We shall try to discover the quantita­ living beings intervene in a thermodynamic :al, tive relations having to do with this inter­ system. We shall see that this depends on a ;he ventiOl). certain type of coupling between different ill­ Smoluchowski (1914, p. 89) writes: "As parameters of the system. We shall consider lIS far as w(' know today, there is no automatic, an unusually simple type of these ominous In, permalJently effective perpetual motion ma­ couplings.! For brevity we shall talk about a va­ chine, in spite of the moleculal' fluctuations, "measurement," if we succeed in coupling )n­ but 8\1('h a device might, perhaps, function the value of a parameter y. (for instance' the ely regularly if it were appropriately operated by position co-ordinate of a pointer of a meas­ ec­ intelligent beings...." uring instrument) at one moment with the Lye A perpetual motion machine therefore is simultaneous value of a fluctuating parame­ igi­ possible if-according to the general method ter x of the system, in such a way that, from rho of physics-we view the experimenting man the value y, we can draw conclusions about ow as a sort of deus ex machina, one who is con­ the value that :/.; had at the moment of the be tinuously and exactly informed of the exist­ "measurement." Then let :I.; and y be un­ 'in­ ing state of nature and who is able to start or coupled after the measurement, so that x can ue­ intel'l'upt the macroscopic course of nature change, while y retains its value for some [lot at any moment without expenditure of work. time. Such measurements are not harmless the Therefore he would definitely not have to interventions. A system in which such md possess the ability to eatch single molecules measurements occur shows a sort of memory like }laxwell's demon, although he would the definitely be different from real living beings I The author e"identlY uses the word "omi­ ell- nous" in the sense that the possibility of realizing in possessing the abo\-e abilities. In eliciting the proposed arrangement threatens the validity any physical effect by action of the sensory of the Second Law.-T,;anslalo/, 126 Maxwell's Demon faculty, in the sense that one can recognize However, it is no longer constrailH'd to the by the state parameter y what value another upper part of the cylinder but bOUIH'PS many tion 01 state parameter :1' had at an earlier moment, times against the piston whieh is already tion c ' and we shall see that simply because of such moving in the I0'ver part of the f·ylinder. III In t a memory the Second Law would be vio­ this way the molecule does a certain amount "'ish t. lated, if the measurement could take place of work on the piston. This is tllt' work that 1. without compensation. We shall realize that corresponds to the isothermal expansion of piston the Second Law is not threatened as much an ideal gas--consisting of ailE' sing;le mole­ the c by this entropy decrease as one would think, cule-from volume VI to tlw volume either as soon as we see that the entropy decrease VI + V 2 • After some time, when the piston choose resulting from the intervention would be has reached the bottom of the container, the ately, compensated completely in any event if the molecule has again the full volume r I + 1-2 restric execution of such a measurement were, for to move about in, and the piston is then re­ ;f < 0 instance, always accompanied by produc­ moved. The procedure can be repeated as 2. r tion of k log 2 units of entropy. In that case many times as desired. The man moves the ment, it will be possible to find a more general piston up or down depending on wlwther the during' entropy law, which applies universally to all molecule is trapped in the upper or lower half down., measurements.