The fluctuation theorem and Lyapunov weights

TL;DR

This paper derives the Fluctuation Theorem using Lyapunov weights instead of Gibbs weights, showing equivalence at long times and extending understanding of entropy fluctuations in small systems.

Contribution

It introduces a novel derivation of the Fluctuation Theorem employing Lyapunov weights, providing an alternative perspective to the standard Gibbs-based approach.

Findings

Fluctuation Theorem derived with Lyapunov weights

Long-time equivalence with Gibbs-based Fluctuation Theorem

Enhanced understanding of entropy fluctuations in small systems

Abstract

The Fluctuation Theorem (FT) is a generalisation of the Second Law of Thermodynamics that applies to small systems observed for short times. For thermostatted systems it gives the probability ratio that entropy will be consumed rather than produced. In this paper we derive the Transient and Steady State Fluctuation Theorems using Lyapunov weights rather than the usual Gibbs weights. At long times the Fluctuation Theorems so derived are identical to those derived using the more standard Gibbs weights.