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arXiv · 2609.00977

Information geometry of non-equilibrium quantum states: Mixed metric structures on an extended information manifold

Kouji Kashiwa·Hidefumi Matsuda
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Abstract

We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics. Using the transverse-field Ising chain model as a laboratory, we investigate the quantum Fisher information metric with particular emphasis on the mixed metric component $g_{ht}$ and related geometric observables, where $h$ is a controllable post-quench Hamiltonian parameter and $t$ is real time. The framework treats $h$ and $t$ as coordinates of an extended information manifold $(h,t)$. The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.

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Kouji Kashiwa, Hidefumi Matsuda. 2026-09-01. Information geometry of non-equilibrium quantum states: Mixed metric structures on an extended information manifold. https://arxiv.org/abs/2609.00977

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