Emergent second law for non-equilibrium steady states

The Gibbs distribution universally characterizes states of thermal equilibrium. In order to extend the Gibbs distribution to non-equilibrium steady states, one must relate the self-information I(x) = -log(P-ss(x)) of microstate x to measurable physical quantities. This is a central problem in non-equilibrium statistical physics. By considering open systems described by stochastic dynamics which become deterministic in the macroscopic limit, we show that changes Delta I = I(x(t)) - I(x(0)) in steady state self-information along deterministic trajectories can be bounded by the macroscopic entropy production Sigma. This bound takes the formof an emergent second law Sigma + k(b)Delta I >= 0, which contains the usual second law Sigma >= 0 as a corollary, and is saturated in the linear regime close to equilibrium. We thus obtain a tighter version of the second law of thermodynamics that provides a link between the deterministic relaxation of a system and the non-equilibrium fluctuations at steady state. In addition to its fundamental value, our result leads to novel methods for computing nonequilibrium distributions, providing a deterministic alternative to Gillespie simulations or spectral methods.

Automated summary

Investigates a central problem in non-equilibrium statistical physics, which is how to extend the Gibbs distribution to non-equilibrium steady states. By considering open systems described by stochastic dynamics, the self-information of microstates is related to macroscopic entropy production, leading to a new version of the second law of thermodynamics that links deterministic relaxation and non-equilibrium fluctuations.