Macroscopic stochastic thermodynamics

Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and an extensive thermodynamics at the macroscopic level are identified. Large deviations theory is then used to build a macroscopic fluctuation theory around this deterministic behavior, which are shown to preserve the fluctuation theorem. For many systems (such as chemical reaction networks, electronic circuits, and 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 quasipotential (or self-information), which is a Lyapunov function for the macroscopic dynamics. Thermodynamics connects the dissipation along deterministic and escape trajectories to the FreidlinWentzell quasipotential, 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, a nonequilibrium fluctuating field theory with its associated thermodynamics is derived. Finally, the macroscopic stochastic dynamics is coarse grained into a Markov jump process describing transitions among deterministic attractors, and the stochastic thermodynamics emerging from it is formulated.