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arXiv · 2510.05823

Mutual entropy and thermal area law in C*-algebraic quantum lattice systems

Hajime Moriya
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Abstract

We present a general definition of quantum mutual entropy for infinitely extended quantum spin and fermion lattice systems. Using this, we establish a thermal area law in these infinitely extended quantum systems. The proof is based on the local thermodynamical stability (LTS), a variational principle in terms of the conditional free energy. Our thermal area law in quasi-local C*-systems applies to general interactions with well-defined surface energies. We also examine the quantum mutual entropy between the left- and right-sided infinite regions of one-dimensional lattice systems. For general translation-invariant finite-range interactions on such systems, the thermal equilibrium state at any temperature exhibits a finite mutual entropy between these infinite disjoint regions. This further implies that the infinitely large quantum entanglement characteristic of critical ground states in one-dimensional systems is drastically destroyed by even a small positive temperature.

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Hajime Moriya. 2025-10-07. Mutual entropy and thermal area law in C*-algebraic quantum lattice systems. https://arxiv.org/abs/2510.05823

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