Entropy production bounds for systems running computer programs

TL;DR

This paper establishes fundamental bounds on entropy production in physical systems executing computer programs, linking thermodynamic costs to computational features and program structure.

Contribution

It introduces a universal lower bound on entropy production, called mismatch cost, and develops a framework to compute minimal thermodynamic costs for running digital programs.

Findings

Mismatch cost scales at least linearly with heat flow in worst case.

Subdividing time intervals can increase the entropy production bound.

Framework applied to compare thermodynamic costs of sorting algorithms.

Abstract

Mismatch cost (MMC) is a universally applicable lower bound on the entropy production (EP) of any fixed physical process across a given time interval. In the first part of the paper, we establish results concerning MMC to prove that it scales at least linearly with the total heat flow in the worst case over initial distributions. We also prove that the MMC lower bound over a given time interval never decreases if the time interval is subdivided into a sequence of sub-intervals, and that the bound often increases. In the second part of the paper, we introduce a general framework for computing the minimal EP (i.e., the MMC) associated with running a computer program on any physical system that implements a modern digital computer. We apply this general framework to compare MMC of running two canonical sorting algorithms, bubble sort and bucket sort. The framework enables us to investigate how thermodynamic cost depends on features like input size and structure (e.g., with or without repeated entries). Finally, we extend the framework to programs that call subroutines.