We propose a method for inferring entropy production (EP) in high-dimensional stochastic systems, including many-body systems and non-Markovian systems with long memory. Standard techniques for estimating EP become intractable in such systems due to computational and statistical limitations. We infer trajectory-level EP and lower bounds on average EP by exploiting a nonequilibrium analogue of the Maximum Entropy principle, along with convex duality. Our approach uses only samples of trajectory observables, such as spatiotemporal correlations. It does not require reconstruction of high-dimensional probability distributions or rate matrices, nor impose any special assumptions such as discrete states or multipartite dynamics. In addition, it may be used to compute a hierarchical decomposition of EP, reflecting contributions from different interaction orders, and it has an intuitive physical interpretation as a "thermodynamic uncertainty relation." We demonstrate its numerical performance on a disordered nonequilibrium spin model with 1000 spins and a large neural spike-train dataset.

翻译：我们提出了一种推断高维随机系统中熵产生的方法，适用于包括多体系统和具有长记忆的非马尔可夫系统。由于计算和统计上的限制，在这些系统中，估计熵产生的标准技术变得难以处理。我们通过利用最大熵原理的非平衡类比以及凸对偶性，推断轨迹层面的熵产生和平均熵产生的下界。我们的方法仅使用轨迹观测量的样本，例如时空相关性。它不需要重建高维概率分布或速率矩阵，也不施加任何特殊假设，如离散状态或多部分动力学。此外，它可用于计算熵产生的层次分解，反映不同相互作用阶数的贡献，并具有作为“热力学不确定性关系”的直观物理解释。我们在一个包含1000个自旋的无序非平衡自旋模型和一个大型神经脉冲序列数据集上展示了其数值性能。