Maxwell demons in phase space

TL;DR

This paper examines the role of phase space properties, specifically Liouville's theorem and adiabatic invariance, in the context of Maxwell's demon and the second law of thermodynamics, highlighting the impact of non-ergodic systems.

Contribution

It analyzes how non-ergodic systems affect phase space invariants and their implications for the second law and Maxwell's demon.

Findings

Enclosed volume is not an adiabatic invariant in non-ergodic systems.

Implications for the second law of thermodynamics.

Analysis of the Szilard engine and related systems.

Abstract

Although there is not a complete "proof" of the second law of thermo- dynamics 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.