On the Asymptotic Convergence of the Transient and Steady State Fluctuation Theorems

TL;DR

This paper uses molecular dynamics simulations to demonstrate that the Transient and Steady State Fluctuation Theorems converge asymptotically in planar Poiseuille flow, with convergence times matching the conditions for the Steady State theorem.

Contribution

It provides evidence that the Transient Fluctuation Theorem converges to the Steady State form on microscopic time scales in non-equilibrium flows.

Findings

Transient and Steady State Fluctuation Theorems converge asymptotically.

Convergence occurs on microscopic time scales.

Convergence time matches the time for the Steady State theorem to hold.

Abstract

Non-equilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the Transient and Steady State forms of the Fluctuation Theorem. In the case of planar Poiseuille flow, we find that the Transient form, valid for all times, converges to the Steady State form on microscopic time scales. Further, we find that the time of convergence for the two Theorems coincides with the time required for satisfaction of the asymptotic Steady State Fluctuation Theorem. PACS numbers: 05.20.-y, 05.70.Ln, 47.10.+g, 47.40.-n