Heat, cold and geometry
July 15, 1983
Classical and relativistic mechanics can be formulated in terms of symplectic geometry; this formulation leads to a rigourous statement of the principle of statistical mechanics and thermodynamics. This analogy also brings to light however certain fundamental difficulties which remain hidden in the traditional approach through some ambiguities.
The “first principle” of thermodynamics can be formulated so to avoid this ambiguity provided one accepts a detour through the principle of general relativity and the Einstein equations for gravitation.
The “second principle” can be satisfied if we accept  a particular geometrical status for temperature and entropy. It is a model of relativistic dissipative continuous medium, which statisfies these two principle, which is presented here.

Patrick Iglesias &  Jean-Marie Souriau, Heat, Cold and Geometry. Published by Cahen et al. (eds), Differential Geometry and Mathematical Physics, pp. 37-68, 1983 by D. Reidel Publishing Company. You can also download the French Version here : “Le Chaud, le Froid et la Géométrie”