Thermal entropy in Calabi-Yau quantum mechanics. (English) Zbl 1539.81020
Summary: 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.
MSC:
| 81P17 | Quantum entropies |
| 80A10 | Classical and relativistic thermodynamics |
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
| 14H25 | Arithmetic ground fields for curves |
| 82B40 | Kinetic theory of gases in equilibrium statistical mechanics |
| 15A16 | Matrix exponential and similar functions of matrices |
| 35B38 | Critical points of functionals in context of PDEs (e.g., energy functionals) |
| 35P10 | Completeness of eigenfunctions and eigenfunction expansions in context of PDEs |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
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