Note on Phase Space Contraction and Entropy Production in Thermostatted Hamiltonian Systems

TL;DR

This paper investigates the relationship between phase space contraction and entropy production in thermostatted Hamiltonian systems, highlighting conditions for their equality and implications for thermodynamic transport coefficients.

Contribution

It analyzes the conditions under which phase space contraction equals entropy production, especially in large systems, and discusses implications for thermodynamics and transport coefficients.

Findings

Equality of rates for constant kinetic energy states regardless of particle number

Large particle number needed for equality in total energy states

Numerical results for Lorentz gas support theoretical analysis

Abstract

The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state are considered. While for stationary states with a constant kinetic energy the two rates are formally equal for all numbers of particles N, for stationary states with constant total (kinetic and potential) energy this only obtains for large N. However, in both cases a large number of particles is required to obtain equality with the entropy production rate of Irreversible Thermodynamics. Consequences of this for the positivity of the transport coefficients and for the Onsager relations are discussed. Numerical results are presented for the special case of the Lorentz gas.