The Generalized Arrhenius Law in Out of Equilibrium Systems

TL;DR

This paper extends the classical Arrhenius law to out-of-equilibrium systems driven by non-conservative forces, revealing new relationships with fluctuation theorems and characterizing noise-activated trajectories.

Contribution

It introduces a generalized Arrhenius law for non-equilibrium systems, linking it to time-reversal symmetry and providing explicit forms for activation trajectories.

Findings

Generalized Arrhenius law for non-equilibrium systems derived

Explicit expressions for noise-activated trajectories obtained

Connection established between the law and fluctuation theorems

Abstract

In this work we provide a comprehensive analysis of the activation problem out of equilibrium. We generalize the Arrhenius law for systems driven by non conservative time independent forces, subjected to retarded friction and non-Markovian noise. The role of the energy function is now played by the out of equilibrium potential {\phi} = -lim_{T{\to}0} T log P_s, with P_s being the steady state probability distribution and T the strength of the noise. We unveil the relationship between the generalized Arrhenius law and a time-reversal transformation discussed in the context of fluctuations theorems out of equilibrium. Moreover, we characterize the noise-activated trajectories by obtaining their explicit expressions and identifying their irreversible nature. Finally, we discuss a real biological application that illustrates our results.