Inferring entropy production in many-body systems using nonequilibrium MaxEnt

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 correlation functions). It does not require reconstruction of high-dimensional probability distributions or rate matrices, nor any special assumptions such as discrete states or multipartite dynamics. It may be used to compute a hierarchical decomposition of EP, reflecting contributions from different kinds of interactions, 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.

Speed-accuracy trade-off for the diffusion models: Wisdom from nonequlibrium thermodynamics and optimal transport

We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Based on the techniques of stochastic thermodynamics, we derive the speed-accuracy trade-off for the diffusion models, which is a trade-off relationship between the speed and accuracy of data generation in diffusion models. Our result implies that the entropy production rate in the forward process affects the errors in data generation. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the conservative force in stochastic thermodynamics and the geodesic of space by the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy trade-off for the diffusion models with different noise schedules such as the cosine schedule, the conditional optimal transport, and the optimal transport.