Maxwell demons in phase space
Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid, 28040 Madrid, Spain
Received: 18 November 2014
Revised: 7 May 2015
Published online: 17 July 2015
Although there is not a complete “proof” of the second law of thermodynamics based on microscopic dynamics, two properties of Hamiltonian systems have been used to prove the impossibility of work extraction from a single thermal reservoir: Liouville's theorem and the adiabatic invariance of the volume enclosed by an energy shell. In this paper we analyze these two properties in the Szilard engine and other systems related with the Maxwell demon. In particular, we recall that the enclosed volume is no longer an adiabatic invariant in non ergodic systems and explore the consequences of this on the second law. This article is supplemented with comments by H. Ouerdane and Lawrence S. Schulman and a final reply by the authors.
© EDP Sciences, Springer-Verlag, 2015