A probabilistic formulation of irreversible kinetics is introduced in which incrementally admissible histories are weighted by a Gibbs-type measure built from an energy-dissipation action and observation constraints, with Theta controlling epistemic uncertainty. This measure can be interpreted as a Bayesian posterior over histories. In the zero-uncertainty limit, it concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution by incremental minimization in the convex generalized-standard-material setting, while allowing multiple competing MAP histories for non-convex energies or temporally coupled constraints. This emergence is demonstrated across seven distinct forward-in-time examples and an inverse inference problem of unknown histories from sparse observations via a global constrained minimum-action principle.

翻译：本文提出了一种不可逆动力学的概率论表述，其中增量容许历史由基于能量耗散作用量与观测约束构建的吉布斯型测度进行加权，参数Theta控制认知不确定性。该测度可解释为历史轨迹上的贝叶斯后验分布。在不确定性趋于零的极限下，测度集中于最大后验（MAP）历史轨迹：在凸广义标准材料框架下，通过增量最小化过程恢复了经典确定性演化规律；而对于非凸能量或时间耦合约束情形，则允许多个竞争性MAP历史共存。这一涌现现象通过七个不同的正向时间演化算例得以验证，并借助全局约束最小作用量原理，解决了基于稀疏观测反演未知历史轨迹的逆向推断问题。