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Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions
Ghofrane Bel-Hadj-Aissa1, Matteo Gori2, Vittorio Penna3
1Dipartimento di Scienze fisiche, della Terra e dell'ambiente (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study reveals how geometric properties of phase space, specifically extrinsic curvatures, predict thermodynamic observable behaviors. Changes in geometry at phase transitions offer fundamental insights into these critical phenomena.
Area of Science:
- Statistical Mechanics
- Geometric Mechanics
- Thermodynamics
Background:
- Thermodynamic observables are crucial for understanding system behavior.
- Phase transitions represent critical points where system properties change dramatically.
- Geometric properties of phase space have been explored for their relation to thermodynamics.
Purpose of the Study:
- To establish a connection between the geometry of phase space and thermodynamic observables.
- To investigate how geometric changes in phase space relate to phase transitions.
- To analyze microcanonical and geometrical descriptions of phase transitions in specific models.
Main Methods:
- Deducing functional forms of thermodynamic observables from geometric properties.
- Utilizing extrinsic curvatures of energy level sets of the Hamiltonian.
- Examining the special case of \u03d5 4 models with nearest-neighbor and mean-field interactions.
Main Results:
- The functional form of thermodynamic observables can be derived from phase space geometry.
- Peculiar behaviors of thermodynamic observables at phase transitions are linked to fundamental changes in the geometry of energy level sets.
- Geometrical descriptions of phase transitions provide insights into microcanonical descriptions.
Conclusions:
- Geometric properties of phase space offer a powerful tool for understanding thermodynamics.
- Phase transitions are fundamentally rooted in geometric alterations within phase space.
- The study provides a novel geometrical perspective on phase transitions in \u03d5 4 models.
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