# Operational derivation of Boltzmann distribution with Maxwell’s demon model

## TL;DR

This paper uses a model of Maxwell's demon to derive the Boltzmann distribution in equilibrium and explore non-equilibrium processes in statistical mechanics.

## Contribution

A novel operational derivation of the Boltzmann distribution without assuming maximum entropy, using a computational demon model.

## Key findings

- The Boltzmann distribution in equilibrium is derived operationally using a Turing-machine demon model.
- The model demonstrates the dissipation-fluctuation relation for non-equilibrium processes.
- The approach avoids assuming the principle of maximum entropy.

## 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.