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Abstract
In order to reconcile the entropy reduction of a system through external interventions that are linked to a measurement with the second law of thermodynamics, there are two main proposals: (i) The entropy reduction is compensated by the entropy increase as a result of the measurement on the system (“Szilard principle"). (ii) The entropy reduction is compensated by the entropy increase as a result of the erasure of the measurement results (“Landauer/Bennett principle"). It seems that the LB principle is widely accepted in the scientific debate. In contrast, in this paper we argue for a modified S principle and criticize the LB principle with regard to various points. Our approach is based on the concept of “conditional action", which is developed in detail. To illustrate our theses, we consider the entropy balance of a variant of the well-known Szilard engine, understood as a classical mechanical system.
Highlights
One chamber heats up while the other cools down, which appears to reduce the entropy of the overall system and to violate the second law of thermodynamics
One could rightly counter that the erasure of a memory content is by no means thermodynamically innocent, but is only possible at the cost of an entropy increase in the environment (L(andauer) principle). We find that the L principle correctly supports the argument that the Szilard process is not a perpetuum mobile of the 2nd kind (PM2)
Taking into account a general time evolution of the combined system A given by a doubly-stochastic transition matrix we may formulate this result as a modified S principle: Principle 1 (Modified S principle) If a conditional action on a system is modeled by an interaction with an apparatus A the decrease in entropy H ( ) is at least compensated by the increase in entropy H (A) of the apparatus A minus the mutual information H f in( : A)
Summary
Since its conception in 1867, James Clerk Maxwell’s thought experiment has inspired countless ideas and probably spawned over a thousand scientific papers [1]. In this famous scenario, an intelligent and skillful being (later called a “demon" by William Thomson) controls a small door between two gas chambers. When individual gas molecules approach the door, the demon selectively opens and closes it. This allows only the fast molecules to enter one chamber, while the slower ones are directed into the other. Numerous works have attempted to rescue the second law by either debunking Maxwell’s thought experiment as impossible or discovering hidden entropy-increasing
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