Classical Thermodynamics and Quantum Statistics

Laszlo Tisza

Yoshimasa Kurihara, Khiem Hong Phan, Nhi My Uyen Quach

On the basis of the theory of thermodynamics, a new formalism of classical nonrelativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on a (1+n)-dimensional smooth manifold are geometrically treated as dynamical variables. The statistical mechanics of particle trajectories are constructed in a classical manner. Thermodynamic variables are introduced through a partition function based on a canonical ensemble of trajectories. Within this theoretical framework, classical mechanics can be interpreted as an equilibrium state of statistical mechanics. The relationship between classical and quantum mechanics is discussed from the viewpoint of statistical mechanics. The maximum-entropy principle is shown to provide a unified view of both classical and quantum mechanics.

Peter Hertel

N. N. Bogolyubov, A. M. Kurbatov, A. S. Shumovskiǐ

Peter Talkner A, Peter Hänggi A

The question of how classical systems approach thermal equilibrium is as old as the foundations of thermodynamics and statistical mechanics. How quantum systems decohere and thermalize is even more puzzling. This Colloquium provides an account of how the thermal equilibrium of a system is influenced by the presence of a thermal bath. It also gives a view of both classical and quantum aspects providing an understanding on the particularities of the quantum case. Moreover, a description of the challenges in the definition of heat from the perspective of fluctuating thermodynamical potentials is given. An old subject, perhaps, but definitely fundamental.

Jurij Avsec, Milan Marčič