# Imitating non-equilibrium steady states using time-varying equilibrium force in many-body diffusive systems

## TL;DR

This paper establishes a theoretical link between non-equilibrium steady states and stochastic pumps in many-body diffusive systems, showing how time-varying forces can mimic steady states and revealing a connection to traffic wave phenomena.

## Contribution

It proves the entropy production rate in NESS exceeds that in stochastic pumps under certain conditions and uncovers a novel relation between traffic waves and particle density propagation.

## Key findings

- Entropy production in NESS is greater than in stochastic pumps.
- Time-averaged stochastic pump can imitate NESS particle density and current.
- High density traffic waves propagate against particle current direction.

## Abstract

An equivalence between non equilibrium steady states (NESS) driven by a time-independent force and stochastic pumps (SP) stirred by a time-varying conservative force is studied for general many-body diffusive systems. When the particle density and current of NESS are imitated by SP time-averaged counterparts, we prove that the entropy production rate in NESS is always greater than that of SP, provided that the conductivity of the particle current is concave as a function of the particle density. Searching for a SP protocol that saturates the entropy production bound reveals an unexpected connection with traffic waves, where a high density region propagates against the direction of the particle current.