We study a classical many-particle system with an external control represented by a time dependent parameter in a Lagrangian. . We show that thermodynamic entropy of the system is the Noether invariant associated with a symmetry for an infinitesimal non-uniform time translation t->t+ eta hbar beta, where eta is a small parameter, hbar is the Planck constant, beta is the inverse temperature that depends on the energy, and trajectories in the phase space are restricted to those consistent with quasi-static processes in thermodynamics. This work was done in collaboration with Yuki Yokokura. See http://arxiv.org/abs/1509.08943 as a reference.

Kyoto University