Revisiting the Monge problem in the Landauer limit

TL;DR

This paper explores the Monge mass transportation problem within stochastic thermodynamics, focusing on the Landauer limit in finite-time processes, and demonstrates efficient numerical solutions in one dimension with implications for computer optimization.

Contribution

It provides a numerical approach to solving the Monge problem in one dimension related to the Landauer limit, linking optimal transport to thermodynamic process optimization.

Findings

Optimal transportation in 1D can be efficiently solved numerically.

The results have implications for optimizing computational processes.

The study bridges mass transport theory with thermodynamic limits.

Abstract

We discuss the Monge problem of mass transportation in the framework of stochastic thermodynamics and revisit the problem of the Landauer limit for finite-time thermodynamics, a problem that got the interest of Krzysztof Gawedzki in the last years. We show that restricted to one dimension, optimal transportation is efficiently solved numerically by well known methods from differential equations. We add a brief discussion about the relevance this has on optimising the processing in modern computers.