Schwinger-Dyson identities are given a geometric reading in which their violations are controlled by the score-mismatch field δs = ∇ log(Q/P_eq), yielding a bound on Fisher information and a tomographic view of probability distortion.
Rugh,Dynamical Approach to Temperature,Phys
3 Pith papers cite this work, alongside 341 external citations. Polarity classification is still indexing.
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abstract
We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the micro canonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a time-average of the functional, div(grad H/|grad H|^2), on the energy-surface. Our method not only yields an efficient computational approach for determining the temperature it also provides an intrinsic link between dynamical systems theory and the statistical mechanics of Hamiltonian systems.
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Configurational temperature estimator from Schwinger-Dyson identity equals 1 in Gross-Witten-Wadia, quartic double-well, and Gaussian ensembles, with finite-N isotropic-anisotropic cancellation and use as Monte Carlo diagnostic.
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Probing Probability Geometry with Schwinger--Dyson Identities: Score Mismatch, Fisher Information, and Configurational Temperature
Schwinger-Dyson identities are given a geometric reading in which their violations are controlled by the score-mismatch field δs = ∇ log(Q/P_eq), yielding a bound on Fisher information and a tomographic view of probability distortion.
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Configurational Temperature in Matrix Models and Random Matrix Ensembles
Configurational temperature estimator from Schwinger-Dyson identity equals 1 in Gross-Witten-Wadia, quartic double-well, and Gaussian ensembles, with finite-N isotropic-anisotropic cancellation and use as Monte Carlo diagnostic.
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