A Gaussian stochastic partition function constrained by gravitational Ward identities yields a proposed generally covariant fluctuating hydrodynamics in which flow is an approximate Killing vector.
Gauge Invariance of Equilibrium Statistical Mechanics
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abstract
We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra, which induces exact sum rules when thermally averaged. Gauge invariance with respect to finite shifting is demonstrated via Monte Carlo simulation in the transformed phase space which generates identical equilibrium averages. Our results point towards a deeper basis of statistical mechanics than previously known and they offer avenues for systematic construction of exact identities and of sampling algorithms.
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Gaussian generally covariant hydrodynamics
A Gaussian stochastic partition function constrained by gravitational Ward identities yields a proposed generally covariant fluctuating hydrodynamics in which flow is an approximate Killing vector.