Thermal Entropy in Calabi-Yau Quantum Mechanics

TL;DR

This paper calculates the high-temperature entropy of quantum systems from mirror curves, revealing insights into quantum gravity and entropy finiteness through asymptotic eigenvalue analysis.

Contribution

It introduces a method to compute the asymptotic von Neumann entropy in mirror curve-derived quantum systems, linking quantum mechanics with quantum gravity concepts.

Findings

Asymptotic entropy matches conventional models at high temperature

Eigenvalue asymptotics inform entropy finiteness

Connections to quantum gravity folklore

Abstract

We consider the von Neumann entropy of a thermal mixed state in quantum systems derived from mirror curves, where the kinetic terms are exponential functions of the momentum operators. Using the mathematical results on the asymptotics of the energy eigenvalues, we compute the asymptotic entropy in high temperature limit and compare with that of the conventional models. We discuss the connections with some folklores in quantum gravity, particularly on the finiteness of entropy.