Occam's Razor Cuts Away the Maximum Entropy Principle

TL;DR

This paper proposes replacing the maximum entropy principle with a phenomenological approach based on the existence of a consistent entropy function, leading to a new axiomatic formulation suitable for non-equilibrium systems.

Contribution

It introduces a novel axiomatic framework for entropy that does not rely on the maximum entropy principle, emphasizing phenomenological consistency.

Findings

Provides a unique construction of probability densities without maximum entropy

Offers an axiomatic formulation of entropy for non-equilibrium phenomena

Suggests a more natural assumption for entropy in microscopic models

Abstract

I show that the maximum entropy principle can be replaced by a more natural assumption, that there exists a phenomenological function of entropy consistent with the microscopic model. The requirement of existence provides then a unique construction of the related probability density. I conclude the letter with an axiomatic formulation of the notion of entropy, which is suitable for exploration of the non-equilibrium phenomena.