Emergent second law for nonequilibrium steady states
Abstract
A longsought generalization of the Gibbs distribution to nonequilibrium steady states $P_\text{ss}(x)$ would amount to relating the selfinformation $\mathcal{I}(x) = \log(P_\text{ss}(x))$ of microstate $x$ to measurable physical quantities. By considering a general class of stochastic open systems with an emergent deterministic dynamics, we prove that changes in $\mathcal{I}(x)$ along deterministic trajectories can be bounded in terms of the entropy flow $\Sigma_e$. This bound takes the form of an emergent second law $\Sigma_e + k_b \Delta \mathcal{I}\geq 0$ which, as we show, is saturated in the linear regime close to equilibrium. A remarkable implication of this result is that the transient deterministic dynamics contains information about the macroscopic fluctuations of nonequilibrium steady states.
 Publication:

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

 Condensed Matter  Statistical Mechanics
 EPrint:
 Corrected error in Figure 1(c) and added new subfigure. Changed to adimensional variables. Added supplementary material