Axiomatic Information Thermodynamics

TL;DR

This paper develops an axiomatic framework for thermodynamics that integrates information as a fundamental element, unifying classical and quantum models and capturing processes involving information acquisition and erasure.

Contribution

It introduces a novel axiomatic system that combines thermodynamics and information theory, allowing for the derivation of entropy with both thermodynamic and informational properties.

Findings

Entropy exhibits both thermodynamic and informational aspects.

The framework supports classical and quantum models.

Probability concepts naturally emerge from the entropy function.

Abstract

We present an axiomatic framework for thermodynamics that incorporates information as a fundamental concept. The axioms describe both ordinary thermodynamic processes and those in which information is acquired, used and erased, as in the operation of Maxwell's demon. This system, like previous axiomatic systems for thermodynamics, supports the construction of conserved quantities and an entropy function governing state changes. Here, however, the entropy exhibits both information and thermodynamic aspects. Although our axioms are not based upon probabilistic concepts, a natural and highly useful concept of probability emerges from the entropy function itself. Our abstract system has many models, including both classical and quantum examples.