# Microreversibility and driven Brownian motion with hydrodynamic long-time correlations

## TL;DR

This paper establishes a nonequilibrium fluctuation theorem for a colloidal particle in hydrodynamic Brownian motion, accounting for long-time correlations and memory effects, and derives related probability distributions and symmetries.

## Contribution

It introduces a generalized Langevin equation with slip boundary conditions and proves a fluctuation theorem for non-Markovian hydrodynamic Brownian motion.

## Key findings

- Hydrodynamic memory effects follow a t^(-3/2) decay.
- Joint probabilities depend only on work and temperature.
- Fluctuation theorem holds despite non-Markovian dynamics.

## Abstract

A nonequilibrium fluctuation theorem is established for a colloidal particle driven by an external force within the hydrodynamic theory of Brownian motion, describing hydrodynamic memory effects such as the t^(-3/2) power-law decay of the velocity autocorrelation function. The generalized Langevin equation is obtained for the general case of slip boundary conditions between the particle and the fluid. The Gaussian probability distributions for the particle to evolve in position-velocity space are deduced. It is proved that the joint probability distributions of forward and time-reversed paths have a ratio depending only on the work performed by the external force and the fluid temperature, in spite of the nonMarkovian character of the generalized Langevin process.