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Nonconcave entropies from generalized canonical ensembles
Marius Costeniuc1, Richard S Ellis, Hugo Touchette
1Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig, Germany. marius.costeniuc@gmail.com
Summary
Calculating nonconcave entropy is challenging. A generalized canonical ensemble, specifically the Gaussian ensemble, successfully computes the nonconcave entropy for the Curie-Weiss-Potts spin model.
Area of Science:
- Statistical mechanics
- Thermodynamics
- Spin models
Background:
- The microcanonical ensemble's entropy is typically derived from the canonical free energy via Legendre transform.
- This method fails when the entropy function is nonconcave.
- A generalized canonical ensemble was recently introduced to address this limitation.
Purpose of the Study:
- To investigate the applicability of a generalized canonical ensemble for calculating nonconcave entropies.
- To study the mean-field Curie-Weiss-Potts spin model.
Main Methods:
- Direct calculations were performed on the mean-field Curie-Weiss-Potts spin model.
- The Gaussian ensemble, a specific instance of the generalized canonical ensemble, was employed.
Main Results:
- The nonconcave entropy of the Curie-Weiss-Potts spin model was successfully obtained.
- Direct calculations confirmed the utility of the Gaussian ensemble for this purpose.
Conclusions:
- The Gaussian ensemble provides a viable method for calculating nonconcave entropies in statistical mechanics.
- This approach overcomes limitations of traditional Legendre transform methods for systems with nonconcave entropy.
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