非高斯活性物质中的熵产生：统一润落定理与深度学习框架

我们提出了一种用于推导由非高斯活性涨动驱动的活性物质系统中熵产生率 (EPR) 的通用框架。通过采用概率流等价技术，我们严格获得了熵产生 (EP) 的分解公式。我们证明，熵产生量 $\Delta s_\mathrm{tot}$ 满足详细润落定理 $\rho_{\mathcal{R}}(\Sigma)/\rho_{\mathcal{R}}(-\Sigma)=e^{\Sigma}$，其中分布 $\rho_{\mathcal{R}}(\Sigma)$ 定义为观察到量 $\mathcal{R}\equiv \Delta s_\mathrm{tot}-B_\mathrm{act}$ 的值的概率，$B_\mathrm{act}$ 为与活性涨动相关的路径依赖随机变量。此外，积分润落定理 $\langle e^{- \mathcal{R} } \rangle = 1$ 以及广义热力学第二定律 $\langle \Delta s_\mathrm{tot} \rangle \ge \langle B_\mathrm{act} \rangle$ 均可直接推导得出。 our results hold under steady-state conditions and can be straightforwardly extended to arbitrary initial states. In the limiting case where active fluctuations vanish, these theorems reduce to the established results of stochastic thermodynamics. Building on this theoretical foundation, we introduce a deep-learning-based methodology for efficiently computing the EP, utilizing the L\'{e}vy score we propose. To illustrate the validity of our approach, we apply it to two representative systems: a Brownian particle in a periodic active bath and an active polymer composed of an active Brownian cross-linker interacting with passive Brownian beads. Our work provides a unified framework for analyzing EP in active matter and offers practical computational tools for investigating complex nonequilibrium behavior.