White-noise fluctuation theorem for Langevin dynamics

TL;DR

This paper introduces a new fluctuation theorem for Langevin dynamics based on white noise statistics, providing a phase-space symmetry that applies broadly and enables versatile parameter inference.

Contribution

It presents a detailed fluctuation theorem derived from Gaussian white noise, independent of phase space distribution, applicable to diverse Langevin systems.

Findings

The theorem applies to each degree of freedom with additive or multiplicative noise.

It is independent of the system's phase space distribution.

Enables a flexible parameter inference algorithm for various systems.

Abstract

Fluctuation theorems based on time-reversal have provided remarkable insight into the non-equilibrium statistics of thermodynamic quantities like heat, work, and entropy production. These types of laws impose constraints on the distributions of certain trajectory functionals that reflect underlying dynamical symmetries. In this work, we introduce a detailed fluctuation theorem for Langevin dynamics that follows from the statistics of Gaussian white noise rather than from time-reversal. The theorem, which originates from a point-wise symmetry in phase space, holds individually for each degree of freedom coupled to additive or multiplicative noise. The relation is independent of the phase space distribution generated by the dynamics and can be used to derive a versatile parameter inference algorithm applicable to the a wide range of systems, including non-conservative and non-Markovian ones.