We present a theoretical framework that reinterprets Population Annealing (PA) through the lens of the discrete-time Schrödinger Bridge (SB) problem. We demonstrate that the heuristic reweighting step in PA is derived by analytically solving the Schrödinger 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.

翻译：我们提出了一个理论框架，将种群退火（PA）重新解释为离散时间薛定谔桥（SB）问题。我们证明，PA中的启发式重加权步骤，是通过瞬时投影解析求解薛定谔系统而导出的，无需迭代计算。此外，我们确定热力学功是解决路径空间全局变分问题的最优控制势。这一视角将非平衡热力学与最优传输的几何框架统一起来，将Jarzynski等式解释为Donsker-Varadhan变分原理中的一致性条件，并阐明了PA的热力学最优性。