Toric nonarchimedean $\mu$entropy and thermodynamical structure
Abstract
We study nonarchimedean $\mu$entropy for toric variety as a further exploration of $\mu$Kstability. We show the existence of optimizer of toric nonarchimedean $\mu^\lambda$entropy for $\lambda \in \mathbb{R}$ and the uniqueness for $\lambda \le 0$. For the proof of existence, we establish a Rellich type compactness result for convex functions on simple polytope. We also reveal a thermodynamical structure on toric nonarchimedean $\mu$entropy. This observation allows us to interpret the enigmatic parameter $T =  \frac{\lambda}{2\pi}$ as temperature and nonarchimedean $\mu$entropy as entropy of an infinite dimensional composite system.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.09090
 arXiv:
 arXiv:2303.09090
 Bibcode:
 2023arXiv230309090I
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 Mathematics  Algebraic Geometry
 EPrint:
 45 pages, comments are very welcome!