Abstract: Recent times have witnessed the rapid development of nonequilibrium thermodynamics, with diverse applications in biological and chemical systems. The central quantity of interest in the field is entropy production (EP), which reflects the overall increase of the entropy of a system and its environment. Major directions of research include (1) tradeoffs between EP and performance measures like speed and precision, (2) inference of EP from empirical observations, and (3) decomposition of EP into contributions from different sources.
In the history of classical thermodynamics, geometric approaches have traditionally played a key role. The geometry of thermodynamic states has been used to study work, EP, and fluctuations in equilibrium and near-equilibrium processes. However, nearly all previous approaches apply only to systems that relax toward equilibrium. This makes them inapplicable to continuously driven systems, including many biological processes, whose long-term behavior is characterized by nonequilibrium steady states, oscillations, and/or chaos.
In this work, we propose a geometric formulation of thermodynamics which is applicable to nonequilibrium systems. To do so, we consider the information geometry of dynamical processes, as specified by one-way transport fluxes, instead of the geometry of thermodynamic states, as usually done. Our formulation leads to new thermodynamic tradeoffs, improved thermodynamic inference, and meaningful decompositions of EP. I will focus in particular on a novel decomposition of EP into “excess” and “housekeeping” contributions, which represent the contributions from conservative and nonconservative forces respectively. The approach will be illustrated using the Brusselator, a well-known minimal model of a chemical oscillator.
(Collaboration with Andreas Dechant, Kohei Yoshimura, Sosuke Ito. arXiv:2206.14599)