RT Journal Article T1 Maxwell demons in phase space A1 Rodríguez Parrondo, Juan Manuel A1 Granger, Léo AB 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. PB Springer Heidelberg SN 1951-6355 YR 2015 FD 2015-07 LK https://hdl.handle.net/20.500.14352/24128 UL https://hdl.handle.net/20.500.14352/24128 LA eng NO © 2015 Springer Heidelberg.This work has been financially supported by Grant ENFASIS (FIS2011-22644, Spanish Government). NO Gobierno de España DS Docta Complutense RD 11 abr 2025