(A) study on learning stochastic thermodynamics from trajectories via neural network

Abstract

Life in nature is inherently both out of equilibrium and stochastic. The conversion of energy through enzymatic activities propels living organisms into a nonequilibrium state, functioning as the fundamental impetus driving all biological processes. Stochastic thermodynamics emerges as a theoretical framework proficient in describing thermodynamic quantities of such nonequilibrium systems at the trajectory level, encompassing applied work on the system, exchanged heat with surrounding environments, and entropy production. This framework has yielded noteworthy results, including fluctuation theorems and thermodynamic uncertainty relations. Despite these theoretical achievements, the analysis of the dynamical and thermodynamic aspects of such systems remains a complex undertaking. The challenge is compounded by the inherent difficulty of handling, arising from the random motion and diminutive size characterizing the entities under investigation. In this thesis, our exploration concentrates on extracting thermodynamic quantities, including entropy production, from observed trajectories or videos of the system. Our initial focus involves a comprehensive examination of nonequilibrium systems by delving into the statistical characteristics of thermodynamic quantities within a widely used stochastic system known as the Brownian gyrator. Specifically, we draw insights for estimating thermodynamic quantities by investigating the intricate relationship between dynamical characteristics and thermodynamic quantities. Secondly, we develop an estimator that measures entropy production from trajectories or recorded videos of the system via neural networks. We rigorously prove that the estimator provides entropy production by optimizing the proposed objective function without detailed knowledge of the system. Finally, reverting to a more fundamental problem, we propose an estimator to infer the equation of motion governing the stochastic system, known as the Langevin equation, and subsequently calculate various thermodynamic quantities. Leveraging Bayesian neural networks, our approach not only provides an accurate Langevin equation of the system but also assesses prediction uncertainties, preventing potential misunderstandings and erroneous decisions about the system. Our research underscores the capabilities of deep learning techniques in analyzing the thermodynamic properties of complex nonequilibrium systems.