Entropy and Correlations in Lattice Gas Automata without Detailed Balance

TL;DR

This paper investigates lattice gas automata lacking detailed balance, focusing on nonlocal interactions, phase transitions, and how to measure entropy and correlations despite the absence of a strict H-theorem.

Contribution

It introduces a notion of locality for nonlocal automata, enabling entropy estimation and correlation measurement in systems without detailed balance.

Findings

Mean-field theory accurately predicts properties away from phase transitions.

Operational definitions of local states allow entropy and correlation estimation.

Nonlocal interactions can produce non-ideal gas behaviors and phase transitions.

Abstract

We consider lattice gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas properties and can undergo phase transitions. For this class of automata, mean-field theory provides a correct evaluation of properties such as compressibility and viscosity (away from the phase transition), despite the fact that no H-theorem strictly holds. We introduce the notion of locality - necessary to define quantities accessible to measurements - by treating the coupling between nonlocal bits as a perturbation. Then if we define operationally ``local'' states of the automaton - whether the system is in a homogeneous or in an inhomogeneous state - we can compute an estimator of the entropy and measure the local channel occupation correlations. These considerations are applied to a simple model with nonlocal interactions.