Out-of-equilibrium inverse temperature is defined as the coordinate of a canonical flow that preserves the state's energy-coherence leaf, and it generically differs from the entropy derivative.
KAM-Stability for Conserved Quantities in Finite-Dimensional Quantum Systems
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We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small perturbations can lead to large deviations over long times, while for robust symmetries their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser (KAM) theorem in classical mechanics. To prove this remarkable result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.
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Temperature Beyond Equilibrium in Isolated Quantum Many-Body Systems and Their Subsystems
Out-of-equilibrium inverse temperature is defined as the coordinate of a canonical flow that preserves the state's energy-coherence leaf, and it generically differs from the entropy derivative.