Operational derivation of Maxwell-Boltzmann distribution with Maxwell's demon model

TL;DR

This paper derives the Maxwell-Boltzmann distribution using an operational model of Maxwell's demon, linking thermodynamics and information theory without relying on maximum entropy, and explores non-equilibrium processes.

Contribution

It provides a novel operational derivation of the Boltzmann distribution using a Turing-machine based demon model, avoiding maximum entropy assumptions.

Findings

Derivation of Boltzmann distribution without maximum entropy

Application of the model to non-equilibrium processes

Demonstration of dissipation-fluctuation relation

Abstract

The resolution of the Maxwell's demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of statistical mechanics and to derive results therein in an "operational" manner. Here, we present a derivation of the Boltzmann distribution in equilibrium as an example, without hypothesizing the principle of maximum entropy. Further, since the model can be applied to non-equilibrium processes, in principle, we demonstrate the dissipation-fluctuation relation to show the possibility in this direction.