Entropy, irreversibility and inference at the foundations of statistical physics

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. When recognized as an inference principle, entropy maximization can be generalized for non-equilibria and applied to path entropies rather than state entropies, becoming the principle of maximum caliber, which we emphasize in this Review. Our primary goal is to enhance crosstalk among researchers working in disparate silos, comparing and contrasting different approaches while pointing to common roots. Entropy is central to statistical physics, but it has multiple meanings. This Review clarifies the strengths of each use and the connections between them, seeking to bolster crosstalk between researchers and to emphasize the power of inference for non-equilibrium physics.