Note on Two Theorems in Nonequilibrium Statistical Mechanics

TL;DR

This paper clarifies the distinctions between two theorems related to phase space trajectories in nonequilibrium statistical mechanics, one by Evans and Searles and another by the authors, highlighting their different focuses and implications.

Contribution

It provides a clear comparison and clarification of two related theorems in nonequilibrium statistical mechanics, emphasizing their differences and specific contexts.

Findings

Distinction between the 1994 Evans-Searles theorem and the 1995 authors' theorem clarified.

Different focuses: trajectory statistics vs. fluctuation statistics in nonequilibrium states.

Enhanced understanding of phase space trajectory theorems in statistical mechanics.

Abstract

An attempt is made to clarify the difference between a theorem derived by Evans and Searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state.