Macroscopic Stochastic Thermodynamics

Abstract: Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and an extensive thermodynamics at the macroscopic level. We then use large deviations theory to build a macroscopic fluctuation theory around this deterministic behavior, which we show preserves the fluctuation theorem. For many systems (e.g. chemical reaction networks, electronic circuits, Potts models), this theory does not coincide with Langevin-equation approaches (obtained by adding Gaussian white noise to the deterministic dynamics) which, if used, are thermodynamically inconsistent. Einstein-Onsager theory of Gaussian fluctuations and irreversible thermodynamics are recovered at equilibrium and close to it, respectively. Far from equilibirum, the free energy is replaced by the dynamically generated quasi-potential (or self-information) which is a Lyapunov function for the macroscopic dynamics. Remarkably, thermodynamics connects the dissipation along deterministic and escape trajectories to the Freidlin-Wentzell quasi-potential, thus constraining the transition rates between attractors induced by rare fluctuations. A coherent perspective on minimum and maximum entropy production principles is also provided. For systems that admit a continuous-space limit, we derive a nonequilibrium fluctuating field theory with its associated thermodynamics. Finally, we coarse grain the macroscopic stochastic dynamics into a Markov jump process describing transitions among deterministic attractors and formulate the stochastic thermodynamics emerging from it.