Inferring entropy production in many-body systems using nonequilibrium MaxEnt
This provides a scalable approach for estimating entropy production in complex systems like biological networks, though it is incremental as it builds on existing thermodynamic principles.
The authors tackled the problem of inferring entropy production in high-dimensional stochastic systems, such as many-body and non-Markovian systems, where standard methods are intractable, and demonstrated their method on a 1000-spin model and a neural spike-train dataset.
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.