Spectral signature of nonequilibrium conditions

TL;DR

This paper reviews how nonequilibrium conditions influence the dynamics of stochastic systems, revealing new behaviors and spectral signatures that distinguish them from equilibrium systems, especially in higher dimensions.

Contribution

It provides a spectral analysis of nonequilibrium stochastic systems, highlighting how external forces alter dynamical regimes and identifying differences from equilibrium behavior.

Findings

Nonequilibrium systems exhibit unique spectral signatures.

Equivalence to equilibrium dynamics holds only for low-dimensional systems (N<5).

Higher-dimensional systems show intrinsically different dynamical behaviors.

Abstract

The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time evolution in various ways. Here we review the dynamics of stochastic systems from the viewpoint of nonequilibrium thermodynamics. We explore the effect of external thermodynamic forces on the possible dynamical regimes and show that the time evolution can become intrinsically different under nonequilibrium conditions. For example, nonequilibrium systems with real dynamical components are similar to equilibrium ones when their state space dimension N < 5, but this equivalence is lost in higher dimensions. Out of equilibrium systems thus present new dynamical behaviors with respect to their equilibrium counterpart. We also study the dynamical modes of generalized, non-stochastic evolution operators such as those arising in counting statistics.