发表机构
University of Padova; INFN, Sezione di Padova; Max Planck Institute for the Physics of Complex Systems; Ludwig-Maximilians-Universität München（帕多瓦大学; 意大利国家核物理研究所帕多瓦分部; 马克斯·普朗克复杂系统物理研究所; 慕尼黑大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
CYNAR 是一种基于轨迹分解的熵产生率估计器，通过流量项与流入率从下方界定熵产生，在多种系统中比传统通量法更可靠，并适用于高维与部分观测场景。
AI 中文摘要
从记录轨迹中推断熵产生率 $\sigma$ 是随机热力学中的一个关键挑战。在实验中，控制动力学的力通常是未知的，并且往往只能观察到系统的一部分自由度。基于最近引入的一种方法 [I. Di Terlizzi, Phys. Rev. Lett. 135, 237101 (2025)]，我们开发并验证了 CYNAR（计算产生非平衡分析与重建），这是一个从轨迹估计 $\sigma$ 的流程。它利用 $\sigma$ 的动力学分解，将其分为从相关函数的短时曲率推断出的流量项 ${\cal T}$ 和从稳态得分（即对数密度的梯度）计算出的流入率 ${\cal G}$。我们证明，在任意观测坐标子集上评估的相同分解，对于任何扩散张量且无需知道隐藏自由度，总是从下方界定 $\sigma$。然后，我们将 CYNAR 与一种更标准的从稳态概率流估计 $\sigma$ 的方法在四个复杂度递增的系统上进行比较。CYNAR 被证明更可靠，在接近平衡时没有可检测的偏差，对空间离散化依赖性弱，并且对测量噪声具有显著的鲁棒性。它也易于应用于高维系统，其中仅流量项就提供了接近 $\sigma$ 的下界，并且在部分观测下仍然提供信息，包括基于通量的估计完全消失的情况。CYNAR 作为开源 Python 包提供。
英文摘要
Inferring the entropy production rate $σ$ from recorded trajectories is a key challenge in stochastic thermodynamics. In experiments, the forces governing the dynamics are usually unknown and often only some of the system's degrees of freedom can be observed. Building on a recently introduced method [I. Di Terlizzi, Phys. Rev. Lett. 135, 237101 (2025)], we develop and validate CYNAR (computation yields nonequilibrium analysis and reconstruction), a pipeline that estimates $σ$ from trajectories. It exploits a kinetic decomposition of $σ$ into a traffic term ${\cal T}$, inferred from the short-time curvature of correlation functions, and an inflow rate ${\cal G}$, computed from the steady-state score, i.e., the gradient of the log-density. We show that the same decomposition, evaluated on any subset of observed coordinates, always bounds $σ$ from below, for any diffusion tensor and without knowledge of the hidden degrees of freedom. We then compare CYNAR with a more standard approach that estimates $σ$ from steady-state probability currents, on four systems of increasing complexity. CYNAR proves to be more reliable, with no detectable bias close to equilibrium, weak dependence on spatial discretization, and marked robustness to measurement noise. It is also readily applicable to high-dimensional systems, where the traffic alone provides a lower bound close to $σ$, and remains informative under partial observation, including cases where the flux-based estimate vanishes identically. CYNAR is provided as an open-source Python package.
Comments18 pages, 10 figures, updated introduction
