# Stochastic efficiency of thermodiffusion: an extended local equilibrium approach

## TL;DR

This paper develops a stochastic model for coupled heat and matter transport at small scales, analyzing efficiency fluctuations and their distributions using fluctuating hydrodynamics, with implications for various thermodynamic systems.

## Contribution

It introduces a mesoscopic stochastic model based on fluctuating hydrodynamics to study efficiency distributions in thermodiffusion, extending the local equilibrium approach.

## Key findings

- Bimodal efficiency distributions can occur under certain conditions.
- Efficiency fluctuations evolve distinctly in large-size and long-time limits.
- Results are applicable to a broad class of systems with ratio-based efficiencies.

## Abstract

The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell connected to two macroscopic reservoirs of heat and particles is developed, based on fluctuating hydrodynamics. Within this approach, the fluctuating separation and thermodynamic efficiencies are defined. The conditions required to observe bimodal distributions of these efficiencies are determined, and the evolution of these distributions is investigated in the large-size and in the long-time limits. The results obtained are not restricted to thermodiffusion and can be generalized to systems where efficiency is defined as a ratio of stochastic state variables or dissipation rates.