# Entropy production for complex Langevin equations

## TL;DR

This paper investigates entropy production in complex-valued Langevin equations modeling nonlinear oscillator networks with non-Hermitian dissipation, providing explicit thermodynamic expressions and analyzing steady states and energy flows.

## Contribution

It introduces a stochastic thermodynamics framework for complex Langevin systems with non-Hermitian terms, deriving explicit entropy production formulas and exploring effects of asymmetric coupling.

## Key findings

- Explicit entropy production rates for complex Langevin networks.
- Steady states characterized by constant entropy production and energy flows.
- Asymmetric coupling influences entropy production significantly.

## Abstract

We study irreversible processes for nonlinear oscillators networks described by complex-valued Langevin equations that account for coupling to different thermo-chemical baths. Dissipation is introduced via non-Hermitian terms in the Hamiltonian of the model. We apply the stochastic thermodynamics formalism to compute explicit expressions for the entropy production rates. We discuss in particular the non-equilibrium steady states of the network characterised by a constant production rate of entropy and flows of energy and particle currents. For two specific examples, a one-dimensional chain and a dimer, numerical calculations are presented. The role of asymmetric coupling among the oscillators on the entropy production is illustrated.