Population Annealing as a Discrete-Time Schr\"odinger Bridge

TL;DR

This paper reinterprets Population Annealing within the discrete-time Schr"odinger Bridge framework, revealing its thermodynamic optimality and connecting non-equilibrium thermodynamics with optimal transport theory.

Contribution

It introduces a novel theoretical perspective that unifies Population Annealing with Schr"odinger Bridges and optimal transport, providing new insights into thermodynamic optimality.

Findings

Reinterprets PA as a Schr"odinger Bridge problem

Identifies thermodynamic work as an optimal control potential

Connects Jarzynski equality with Donsker-Varadhan principle

Abstract

We present a theoretical framework that reinterprets Population Annealing (PA) through the lens of the discrete-time Schr\"odinger Bridge (SB) problem. We demonstrate that the heuristic reweighting step in PA is derived by analytically solving the Schr\"odinger system without iterative computation via instantaneous projection. In addition, we identify the thermodynamic work as the optimal control potential that solves the global variational problem on path space. This perspective unifies non-equilibrium thermodynamics with the geometric framework of optimal transport, interpreting the Jarzynski equality as a consistency condition within the Donsker-Varadhan variational principle, and elucidates the thermodynamic optimality of PA.