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Thermodynamic Entropy as a Noether Invariant from Contact Geometry
Alessandro Bravetti1, Miguel Ángel García-Ariza1, Diego Tapias2
1Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de Mexico, A. P. 70543, Ciudad de Mexico 04510, Mexico.
Entropy (Basel, Switzerland)
|July 29, 2023
Summary
Researchers linked thermodynamic entropy to time-symmetry using Noether's theorem in Hamiltonian systems. For systems at equilibrium, this implies conserved total entropy, offering a geometric perspective on thermodynamics.
Area of Science:
- Thermodynamics
- Geometric Mechanics
- Mathematical Physics
Background:
- Noether's theorem is fundamental in physics, connecting symmetries to conserved quantities.
- Thermodynamic entropy is a key concept in understanding heat, work, and energy dispersal.
- Contact Hamiltonian systems provide a framework for describing dissipative and conservative dynamics.
Purpose of the Study:
- To establish a connection between thermodynamic entropy and Noether invariants in contact Hamiltonian systems.
- To explore the implications of time-translational symmetry for entropy conservation.
- To offer a geometric interpretation of thermodynamic entropy.
Main Methods:
- Application of a specific formulation of Noether's theorem tailored for contact Hamiltonian systems.
- Derivation of a mathematical relationship between thermodynamic entropy and the Noether invariant linked to time-translation symmetry.
- Analysis of the specific case of thermostatted systems at thermodynamic equilibrium.
Main Results:
- A direct relation is derived between thermodynamic entropy and the Noether invariant associated with time-translational symmetry.
- For thermostatted systems in equilibrium, the total entropy of the system and its reservoir is shown to be conserved.
- The findings provide a novel geometric perspective on the nature of thermodynamic entropy.
Conclusions:
- The study successfully links symmetries, via Noether's theorem, to thermodynamic concepts like entropy.
- Conservation of total entropy in equilibrium systems is demonstrated as a consequence of time-translational symmetry.
- The geometric viewpoint enhances the fundamental understanding of thermodynamic entropy in physical systems.
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