Boundary layers in stochastic thermodynamics

TL;DR

This paper investigates how boundary layers affect the optimization of heat and work in stochastic thermodynamics, revealing that regularization transforms protocol jumps into finite-width boundary layers with specific energetic properties.

Contribution

It introduces a regularization method that replaces protocol jumps with boundary layers and links optimal protocols to deterministic transport equations.

Findings

Boundary layers replace jumps with finite width regions.

No heat is dissipated within boundary layers at optimality.

Optimal protocols relate to solutions of the Burgers equation.

Abstract

We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give a new interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).