# The McLennan-Zubarev steady state distribution and fluctuation theorems

## TL;DR

This paper explores the McLennan-Zubarev steady state distribution's connection to fluctuation theorems, deriving key relations and expanding transport coefficients in nonequilibrium thermodynamics.

## Contribution

It derives the steady state distribution from detailed balance and proves fluctuation theorems for entropy and currents, linking them to Onsager's relations and Green-Kubo corrections.

## Key findings

- Derived the McLennan-Zubarev distribution from nonequilibrium detailed balance.
- Proved fluctuation theorems for entropy and currents.
- Expanded current in terms of thermodynamic forces, confirming Onsager's reciprocal relations and deriving Green-Kubo corrections.

## Abstract

The McLennan-Zubarev steady state distribution is studied in the connection with fluctuation theorems. We derive the McLennan-Zubarev steady state distribution from the nonequilibrium detailed balance relation. Then, considering the cumulant function or cumulant functional, two fluctuation theorems for entropy and for currents are proved. Using the fluctuation theorem for currents, the current is expanded in terms of thermodynamic forces. In the lowest order of the thermodynamic force, we find that the transport coefficient satisfies the Onsager's reciprocal relation. In the next order, we derived the correction term to the Green-Kubo formula.