Non-equilibrium systems have steady-state distributions and non-steady dynamics

TL;DR

This paper generalizes the concept of steady states to non-equilibrium systems with sustained currents, defining conditions for their existence and stability, and illustrating with examples.

Contribution

It introduces a generalized framework for steady states in non-equilibrium systems, linking stationary distributions with non-stationary currents.

Findings

Steady states in non-equilibrium systems involve stationary probability densities and deterministic trajectories.

Conditions for the existence and stability of these steady states are precisely characterized.

Examples demonstrate the application of the theoretical framework.

Abstract

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe such systems. In these, the generalisation of a steady state is associated with a stationary probability density of micro-states and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of non-stationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.