Abstract :
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the complementarity between two descriptions that are unified in thermodynamics: (i) the parametrization of the system macrostate in terms of mechanical macroscopic observables image, and (ii) the dynamical description that explains the evolution of a system towards the thermodynamic equilibrium. As expected, such a complementarity is related to the uncertainty relations of classical statistical mechanics image. Here, image is the Boltzmann constant, image are the restituting generalized forces derived from the entropy image of a closed system, which is found in an equilibrium situation driven by certain control parameters image. These arguments constitute the central ingredients of a reformulation of classical statistical mechanics from the notion of complementarity. In this new framework, Einstein postulate of classical fluctuation theory image appears as the correspondence principle between classical statistical mechanics and thermodynamics in the limit image, while the existence of uncertainty relations can be associated with the non-commuting character of certain operators.
