Optimal protocols and optimal transport in stochastic thermodynamics

Abstract

Thermodynamics of small systems has become an important field of statistical physics. They are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in Cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a non-equilibrium transition in finite time is solved by Burgers equation of Cosmology and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

5 pages, RevTex4-1 format

References in corpus (5)

• Optimal finite-time processes in stochastic thermodynamics
• Fluctuation theorems for stochastic dynamics
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• Fluctuation Relations for Diffusion Processes
• Computing the optimal protocol for finite-time processes in stochastic thermodynamics

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