Miguel Aguilera   complex systems, neuroscience and cognition

Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model

Our new paper nonequilibrium thermodynamics of large, disordered networks - in collaboration with Masanao Igarashi and Hideaki Shimazaki - has just been published in Nature Communications. In this study we analytically calculate an exact expression for the entropy production of an asymmetric version of the Sherrington-Kirkpatric model, finding that it is maximized both at critical phase transitions as well as a region of quasi-deterministic chaos.

Thanks to BCAM’s and Kyoto University communication teams we have released a press release describing the interest of looking at neural and complex networks from the perspective of a thermoynamic lens, accompanied by a fantastic illustration by Robin Hoshino

Entropy production spin model illustration

  1. Aguilera, M, Igarashi, M & Shimazaki H (2023). Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model. Nature Communications 14, 3685.


Most natural systems operate far from equilibrium, displaying time-asymmetric, irreversible dynamics characterized by a positive entropy production while exchanging energy and matter with the environment. Although stochastic thermodynamics underpins the irreversible dynamics of small systems, the nonequilibrium thermodynamics of larger, more complex systems remains unexplored. Here, we investigate the asymmetric Sherrington-Kirkpatrick model with synchronous and asynchronous updates as a prototypical example of large-scale nonequilibrium processes. Using a path integral method, we calculate a generating functional over trajectories, obtaining exact solutions of the order parameters, path entropy, and steady-state entropy production of infinitely large networks. Entropy production peaks at critical order-disorder phase transitions, but is significantly larger for quasi-deterministic disordered dynamics. Consequently, entropy production can increase under distinct scenarios, requiring multiple thermodynamic quantities to describe the system accurately. These results contribute to developing an exact analytical theory of the nonequilibrium thermodynamics of large-scale physical and biological systems and their phase transitions.