7th KIAS Conference on Statistical Physics
[Talk 1] Thermodynamic entropy as a Noether invariant
SPEAKER | Shin-ichi Sasa
INSTITUTE | Kyoto University
DATE | July 4(Mon), 2016
TIME | 09:00
PLACE | Korea Institute for Advanced Study (KIAS), Seoul, Korea
ABSTRACT | Entropy is a fundamental concept in physics. It appears in thermodynamics, statistical mechanics,
information theory, computation theory, and thermodynamics of black holes. Recently, the inter-relation
between different types of entropy has been discovered. By synthesizing various aspects of entropy, we
thus obtain a deeper understanding of fundamental laws in physics. Now, there is a paper , which
claims that black hole entropy is obtained as the Noether charge associated with the horizon Killing
field. We are then naturally led to ask whether thermodynamic entropy of standard materials is also
characterized by a Noether invariant.
In the presentation, 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
uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal nonuniform
time translation, where trajectories in the phase space are restricted to those consistent with
quasi-static processes in thermodynamics .
The most remarkable result of our theory is the emergence of a universal constant of the action
dimension, while our theory stands on classical mechanics, classical statistical mechanics, and
 R. M. Wald, Phys. Rev. D 48 R3427 (1993).
 S. Sasa and Y. Yokokura, Phys. Rev. Lett. 116 140601 (2016)