Nonequilibrium Steady-State Free Energy via Optimal Transport

Free energy is a crucial concept in thermodynamics and statistical mechanics: in the former, its changes represent the minimum work required to move a system between two equilibrium states; the latter provides a microscopic definition in terms of the system partition function. Yet many natural phenomena operate far from equilibrium, even in stationary conditions—exhibiting nonequilibrium steady states—and defining an appropriate nonequilibrium steady-state free energy remains elusive.



We aim to build such a notion by combining tools from stochastic thermodynamics and optimal transport theory. We use variational tools from the latter to computationally model optimal protocols—in terms of several relevant stochastic-thermodynamic observables—in toy models exhibiting nonequilibrium steady states, and explore their feasibility to develop a generalized steady-state free energy.