Emergent second law for nonequilibrium steady states
Abstract
The Gibbs distribution universally characterizes states of thermal equilibrium. In order to extend the Gibbs distribution to nonequilibrium steady states, one must relate the selfinformation $\mathcal{I}(x) = \log(P_\text{ss}(x))$ of microstate $x$ to measurable physical quantities. This is a central problem in nonequilibrium statistical physics. By considering open systems described by stochastic dynamics which become deterministic in the macroscopic limit, we show that changes $\Delta \mathcal{I} = \mathcal{I}(x_t)  \mathcal{I}(x_0)$ in steady state selfinformation along deterministic trajectories can be bounded by the macroscopic entropy production $\Sigma$. This bound takes the form of an emergent second law $\Sigma + k_b \Delta \mathcal{I}\geq 0$, which contains the usual second law $\Sigma \geq 0$ as a corollary, and is saturated in the linear regime close to equilibrium. In summary, we obtain a tighter version of the second law of thermodynamics that provides a link between the deterministic relaxation of a system and the nonequilibrium fluctuations at steady state.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.04906
 Bibcode:
 2021arXiv210904906F
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 Slight generalization to include states with internal entropy. Improved explanation and reorganization of the article