Unified, Geometric Framework for Nonequilibrium Protocol Optimization


Controlling thermodynamic cycles to minimize the dissipated heat is a long-standing goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic metric—determined via a linear response approach—can be directly derived from the same objective function that is optimized in the optimal transport problem, thus providing a unified perspective on thermodynamic geometries. We investigate this unified geometric framework in two model systems and observe that our procedure for optimizing control protocols is robust beyond linear response.

Physical Review Letters