We investigate gauge invariance against phase space shifting in
nonequilibrium systems, as represented by time-dependent many-body Hamiltonians
that drive an initial ensemble out of thermal equilibrium. The theory gives
rise to gauge correlation functions that characterize spatial and temporal
inhomogeneity with microscopic resolution on the one-body level. Analyzing the
dynamical gauge invariance allows one to identify a specific localized shift
gauge current as a fundamental nonequilibrium observable that characterizes
particle-based dynamics. When averaged over the nonequilibrium ensemble, the
shift current vanishes identically, which constitutes an exact nonequilibrium
conservation law that generalizes the Yvon-Born-Green equilibrium balance of
the vanishing sum of ideal, interparticle, and external forces. Any given
observable is associated with a corresponding dynamical hyperforce density and
hypercurrent correlation function. An exact nonequilibrium sum rule
interrelates these one-body functions, in generalization of the recent
hyperforce balance for equilibrium systems. We demonstrate the physical
consequences of the dynamical gauge invariance using both harmonically confined
ideal gas setups, for which we present analytical solutions, and molecular
dynamics simulations of interacting systems, for which we demonstrate the shift
current and hypercurrent correlation functions to be accessible both via
finite-difference methods and via trajectory-based automatic differentiation.
We show that the theory constitutes a starting point for developing
nonequilibrium reduced-variance sampling algorithms and for investigating
thermally-activated barrier crossing.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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