Ying-Jen Yang

Abstract The great power of equilibrium statistical physics comes from its principled foundations: its First Law (conservation), Second Law (variational tendency principle), and its Legendre Transforms from observables (U, V, N) to their driving forces (T, p, μ). Here, we generalize this structure to nonequilibria in Caliber Force Theory, replacing state entropies with path entropies; and replacing (U, V, N) with dynamic observables (node probabilities, edge traffics, and cycle fluxes).

Abstract Statistical physics relates the properties of macroscale systems to the distributions of their microscale agents. Its central tool has been the maximization of entropy, an equilibrium variational principle. Recent work has sought extensions to non-equilibria: across processes of change both fast and slow, in the Jarzynski equality and fluctuation relations and other tools of stochastic thermodynamics, using large deviation theory or others.

Abstract A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent, components contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future.