Nonequilibrium statistical physics study using deep learning

Abstract

we also studied to find out the optimal mechanism for maximizing the work of such systems. First, we developed the neural estimator for entropy production (NEEP), a novel method for inferring entropy production (EP) in a nonequilibrium process. While EP is a key quantity in stochastic thermodynamics to describe the energetics of the process, it is difficult to measure using the conventional methods due to the curse of dimensionality when the system has high degrees of freedom. Our NEEP can efficiently address this problem by using deep learning. In particular, this method estimates EP with only trajectory data of the relevant variables, without information about the underlying mechanism of the process. Next, we studied through deep reinforcement learning what the optimal mechanism would be for the nonequilibrium system to perform work optimally. To be specific, we investigated the transport phenomena in small biological systems that have been described by a collective flashing ratchet model. This model transports particles using an asymmetric potential, and the net current of the particles can be increased by feedback control based on the particle positions. Several feedback strategies for maximizing the current have been proposed, but optimal policies have not been reported for a moderate number of particles. The results showed that policies discovered by deep reinforcement learning outperform the previous policies. Moreover, we demonstrated this approach by application to a time-delayed feedback situation that occurs in actual experiments. Our AI-based approaches presented in this thesis are expected to be useful for understanding complex nonequilibrium systems in nature.

Numerous systems in nature, such as biological systems and active matter, use the energy of fuels in the surrounding environment to perform work through nonequilibrium processes. For example, all life phenomena occur by consuming a fuel called ATP. To understand such processes, we should describe the transformation process between work and heat with thermodynamics. In this thesis, we developed a new method to measure generated heat in the nonequilibrium process of complex systems with high degrees of freedom using deep learning