Entropy, heat, and G\"odel incompleteness

TL;DR

This paper explores the connection between irreversibility in thermodynamics and G"odel incompleteness, proposing that the fundamental limits of information in complex systems may explain entropy and heat production.

Contribution

It introduces a novel perspective linking G"odel incompleteness to thermodynamic irreversibility, suggesting a fundamental informational basis for entropy production.

Findings

Irreversible phenomena stem from complex reversible dynamics.

G"odel incompleteness may underpin the impossibility of tracking dynamics.

Implications for the foundations of physics and mathematics.

Abstract

Irreversible phenomena, such as the production of entropy and heat, arise from fundamental reversible dynamics because the forward dynamics is too complex, in the sense that it becomes impossible to provide the necessary information to keep track of the dynamics. On a heuristic level, this is well captured by coarse graining. We suggest that on a fundamental level the impossibility to provide the necessary information might be related to the incompleteness results of G\"odel. This would hold interesting implications for both, mathematics and physics.