Boltzmannian Equilibrium in Stochastic Systems

TL;DR

This paper extends the concept of Boltzmannian equilibrium to stochastic systems, proving that equilibrium macro-regions are large in a probabilistic sense, thus generalizing previous deterministic results.

Contribution

It introduces stochastic versions of Boltzmannian equilibrium notions and proves key theorems demonstrating the prominence of equilibrium macro-regions in stochastic systems.

Findings

Established stochastic equivalents of the Dominance and Prevalence Theorems.

Proved that equilibrium macro-regions are large in stochastic systems.

Extended deterministic equilibrium concepts to stochastic micro-dynamics.

Abstract

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-varepsilon-equilibrium (Werndl and Frigg 2015a, 2015b). This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic systems equilibrium macro-regions are large in requisite sense.