Thermodynamics as Combinatorics: A Toy Theory

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.