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Szilard-1929.Pdf In memory of Leo Szilard, who passed away on May 30,1964, we present an English translation of his classical paper ober die Enfropieuerminderung in einem thermodynamischen System bei Eingrifen intelligenter Wesen, which appeared in the Zeitschrift fur Physik, 1929,53,840-856. The publica- tion in this journal of this translation was approved by Dr. Szilard before he died, but he never saw the copy. At Mrs. Szilard’s request, Dr. Carl Eckart revised the translation. This is one of the earliest, if not the earliest paper, in which the relations of physical entropy to information (in the sense of modem mathematical theory of communication) were rigorously demonstrated and in which Max- well’s famous demon was successfully exorcised: a milestone in the integra- tion of physical and cognitive concepts. ON THE DECREASE OF ENTROPY IN A THERMODYNAMIC SYSTEM BY THE INTERVENTION OF INTELLIGENT BEINGS by Leo Szilard Translated by Anatol Rapoport and Mechthilde Knoller from the original article “Uber die Entropiever- minderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen.” Zeitschrift fur Physik, 1929, 65, 840-866. 0*3 resulting quantity of entropy. We find that The objective of the investigation is to it is exactly as great as is necessary for full find the conditions which apparently allow compensation. The actual production of the construction of a perpetual-motion ma- entropy in connection with the measure- chine of the second kind, if one permits an ment, therefore, need not be greater than intelligent being to intervene in a thermo- Equation (1) requires. dynamic system. When such beings make F(J measurements, they make the system behave in a manner distinctly different from the way HERE is an objection, already historical, a mechanical system behaves when left to Tagainst the universal validity of the itself. We show that it is a sort of a memory Second Law of Thermodynamics, which in- faculty, manifested by a system where deed looks rather ominous. The objection is measurements occur, that might cause a embodied in the notion of Maxwell’s demon, permanent decrease of entropy and thus a who in a different form appears even nowa- violation of the Second Law of Thermody- days again and again; perhaps not unreason- namics, were it not for the fact that the ably, inasmuch as behind the precisely measurements themselves are necessarily formulated question quantitative connec- accompanied by a production of entropy. At tions seem to be hidden which to date have first we calculate this production of entropy not been clarified. The objection in its origi- quite generally from the postulate that full nal formulation concerns a demon who compensation is made in the sense of the catches the fast molecules and lets the slow Second Law (Equation [l]).Second, by ones pass. To be sure, the objection can be using an inanimate device able to make met with the reply that man cannot in prin- measurements-however under continual ciple foresee the value of a thermally fluc- entropy production-we shall calculate the tuating parameter. However, one cannot Requests for reprints of this paper should be deny that we can very well measure the sent to: value of such a fluctuating parameter and Mrs. Leo Szilard 2380 Torrey Pines Road therefore could certainly gain energy at the La Jolla, California 92038 expense of heat by arranging our interven- 301 302 LEO SZILAHI) tiori according to the results of the ineasure- as well as the motor nervous systems a nients. Presently, of course, we do not know degradation of energy is always involved, whether we commit an error by not includ- quite apart from the fact that the very ing the intervening man into the system and existence of a nervous system is dependent by disregarding his biological phenomena. on continual dissipation of energy. Apart froin this unresolved matter, it is Whether-considering these circuin- known today that in a system left to itself no stances---real living beings could continually “perpetuuni mobile’’ (perpetual niotion ma- or at least regularly produce energy at the chine) of the second kind (more exactly, no expense of heat of the lowest temperature ap- “automatic machine of continual finite pears very doubtful, even though our ignor- work-yield which uses heat at the lowest ance of the biological phenomena does not temperature”) can operate in spite of the allow a definite answer. However, the latter fluctuation phenomena. A perpetuuni mobile questions lead beyond the scope of physics would have to be a machine which in the in the strict sense. long run could lift a weight at the expense of It appears that the ignorance of the bio- thc heat content of a reservoir. In other logical phenomena need not prevent us frorn words, if we want to use the fluctuation phe- understanding that which seems to us to be noinena in order to gain energy at the ex- the essential thing. We may be sure that pense of heat, we are in the same position as intelligent living beings-insofar as we are playing a ganic of chance, in which we may dealing with their intervention in a ther- win certain amounts now and then, although niodynaniic systen-can be replaced by non- the expectation value of the winnings is zero living devices whose “biological phenomena” or negat>ive.The same applies to a system one could follow and determine whether in where the intervention from outside is per- fact a compensation of the entropy decrease formed strictly periodically, say by periodi- takes place as a result of the intervention by cally moving machines. We consider this as such a device in a system. established (Szilard, 1925) and intend here In the first place, we wish to learn what only to consider the difficulties that occur circumstance conditions the decrease of when intelligent beings intervene in a sys- entropy which takcs place when intelligent tem. We shall try to discover the quantita- living beings intervene in a therniodynamic tive relations having to do with this inter- system. We shall see that this depends on a vention. certain type of coupling between different Snioluchowski (1914, p. 89) writes: “As parameters of the system. We shall consider far as we know today, there is no automatic, an unusually simple type of these ominous permanently effective perpetual motion ma- coup1ings.l For brevity we shall talk about a chine, in spite of the molecular fluctuations, “measurement,” if we succeed in coupling but such a device might, perhaps, function the value of a parameter y (for instance the regularly if it were appropriately operated by position co-ordinate of a pointer of a meas- intelligent beings.. .” uring instrument) at one nioment with the A perpetual motion machine therefore is simultaneous value of a fluctuating parame- possible if-according to the general method ter x of the system, in such a way that, from of physics-we view the experimenting man the value y, we can draw conclusions about as a sort of deus ex machina, one who is con- the value that x had at the moment of the tinuously and exactly informed of the exist- “measurement.” Then let x and y be un- ing state of nature and who is able to start or coupled after the measurement, so that 5 can interrupt the macroscopic course of nature change, while y retains its value for some at any rnornent without expenditure of work. time. Such measurements are not harmless Therefore he would definitely not have to interventions. A system in which such possess the ability to catch single molecules measurements occur shows a sort of memory like Maxwell’s demon, although he would ’The author evidently uses the word “omi- definitely be different from real living beings nous” in the sense that the possibility of realizing in possessing the above abilities. In eliciting the proposed arrangement threatens the validity any physical effect by action of the sensory of the Second Law.-Translator ON THE DECREASEOF ENTROPY 303 faculty, in the sense that one can recognize However, it is no longer constraincd to the by the state parameter y what value another upper part of the cylinder but bounces inany state parameter z had at an earlier moment, times against the piston which is already and we shall see that simply because of such moving in the lower part of the cylinder. In a memory the Second Law would be vio- this way the molecule does a certain amount lated, if the measurement could take place of work on the piston. This is the work that without compensation. We shall realize that corresponds to the isothermal expansion of the Second Law is not threatened as much an ideal gas--consisting of one single mole- by this entropy decrease as one would think, cule-from volume V, to the volume as soon as we see that the entropy decrease V1 + V2 . After some time, when the piston resulting from the intervention would be has reached the bottom of the container, the compensated completely in any event if the molecule has again the full volume V1 + Vz execution of such a measurement were, for to move about in, and the piston is then re- instance, always accompanied by produc- moved. The procedure can be repeated as tion of k log 2 units of entropy. In that case many times as desired. The man moves the it will be possible to find a more general piston up or down depending on whether the entropy law, which applies universally to all molecule is trapped in the upper or lower half measurements. Finally we shall consider a of the piston.
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