Thermodynamics as Combinatorics: A Toy Theory

TL;DR

This paper presents a toy model that derives fundamental thermodynamic laws using binary strings and Hamming weight, offering insights into temperature, equilibrium, and the zeroth law.

Contribution

It introduces a novel combinatorial approach to thermodynamics, linking binary string representations to thermodynamic concepts and laws.

Findings

Reproduces negative temperatures within the model

Shows equilibrium as the coincidence of statistical and structural temperatures

Finds the zeroth law to be redundant and not universally valid

Abstract

We discuss a simple toy model which allows, in a natural way, for deriving central facts from thermodynamics such as its fundamental laws, including Carnot's version of the second principle. Our viewpoint represents thermodynamic systems as binary strings, and it links their temperature to their Hamming weight. From this, we can reproduce the possibility of negative temperatures, the notion of equilibrium as the co\"incidence of two notions of temperature - statistical versus structural -, as well as the zeroth law of thermodynamics (transitivity of the thermal-equilibrium relation), which we find to be redundant, as other authors, yet at the same time not to be universally valid.