Fluctuation theorem for the renormalized entropy change in the strongly nonlinear nonequilibrium regime

TL;DR

This paper extends the fluctuation theorem to strongly nonlinear nonequilibrium systems by introducing a renormalized entropy change, suggesting modifications to the Shannon entropy in such regimes.

Contribution

It generalizes the fluctuation theorem for entropy change in nonlinear regimes using a renormalization approach, building on previous linear theories.

Findings

Fluctuation theorem holds with renormalized entropy in nonlinear regimes.

Ordinary entropy fluctuation theorem is recovered near equilibrium.

Implication that Shannon entropy may need modification in nonlinear nonequilibrium states.

Abstract

Generalizing a recent work [T. Taniguchi and E. G. D. Cohen, J. Stat. Phys. 126, 1 (2006)] that was based on the Onsager-Machlup theory, a nonlinear relaxation process is considered for a macroscopic thermodynamic quantity. It is found that the fluctuation theorem holds in the nonlinear nonequilibrium regime if the change of the entropy characterized by local equilibria is appropriately renormalized. The fluctuation theorem for the ordinary entropy change is recovered in the linear near-equilibrium case. This result suggests a possibility that the the information-theoretic entropy of the Shannon form may be modified in the strongly nonlinear nonequilibrium regime.