Entropy, heat, and G\"odel incompleteness

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.