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Thermodynamic Entropy as a Noether Invariant.
Shin-Ichi Sasa1, Yuki Yokokura2,3
1Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Physical Review Letters
|April 23, 2016
Summary
Thermodynamic entropy is identified as a Noether invariant for classical many-particle systems. This invariant arises from a symmetry in time translation, linking thermodynamics to fundamental physics principles.
Area of Science:
- Classical mechanics
- Statistical mechanics
- Thermodynamics
- Noether's theorem
Background:
- Classical many-particle systems are fundamental in physics.
- Thermodynamic entropy is a key concept in thermodynamics.
- Noether's theorem connects symmetries to conserved quantities.
Purpose of the Study:
- To characterize thermodynamic entropy within a classical many-particle system.
- To explore the connection between symmetries and thermodynamic properties.
- To investigate the role of external control parameters.
Main Methods:
- Utilizing a Lagrangian formulation for the many-particle system.
- Introducing a time-dependent extensive parameter as an external control.
- Analyzing symmetries related to infinitesimal nonuniform time translations.
Main Results:
- Thermodynamic entropy is uniquely identified as a Noether invariant.
- The symmetry corresponds to a specific time translation (t→t+ηℏβ).
- This characterization holds for quasistatic processes in thermodynamics.
Conclusions:
- Establishes a direct link between thermodynamic entropy and Noether invariants.
- Demonstrates the power of symmetry principles in understanding thermodynamic quantities.
- Provides a framework for studying driven classical systems.
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