Nonequilibrium Neural Computation: Stochastic thermodynamics of the asymmetric Sherrington-Kirkpatrick model

Effective neural information processing entails flexible architectures integrating multiple sensory streams that vary in time with internal and external events. Physically, neural computation is, in a thermodynamic sense, an out-of-equilibrium, non-stationary process that changes dynamically giving rise to entropy production. Cognitively, nonequilibrium neural activity results in dynamic changes in sensory streams and internal states. In contrast, classical neuroscience theory focuses on stationary, equilibrium information paradigms (e.g., efficient coding theory), which often fail to describe the role of nonequilibrium fluctuations in neural processes. In consequence, there is a pressing demand for mathematical tools to understand the dynamics of large-scale, non-equilibrium networks systems and to analyse high-dimensional datasets recorded from them. Inspired by the success of the equilibrium Ising model in investigating disordered systems in the thermodynamic limit, we study the nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick system with both synchronous and asynchronous updates as a prototypical model of large-scale nonequilibrium processes. We employ a path integral method to calculate a generating functional over the trajectories to derive exact solutions of the order parameters, conditional entropy of trajectories, and steady-state entropy production of infinitely large networks. Inspecting the system's phase diagram, we find that the entropy production peaks at a critical order-disorder phase transition, but it is more prominent outside the critical regime, especially at disordered phases with low entropy rates. While entropy production is becoming popular to characterize various complex systems, our results reveal that increased entropy production is linked with radically different scenarios, and combining multiple thermodynamic quantities yields a more precise picture of the system. These results contribute to an exact analytical theory for studying the thermodynamic properties of large-scale nonequilibrium systems and their phase transitions.