Geometrical structures of the instantaneous current and their macroscopic effects: vortices and perspectives in non-gradient models

Abstract

First we discuss the definition of the instantaneous current in interacting particle systems, in particular in mass-energy systems and we point out its role in the derivation of the hydrodynamics. Later we present some geometrical structures of the instantaneous current when the rates satisfy a common symmetry. These structures give some new ideas in non-gradient models and show new phenomenology in diffusive interacting particle systems. Specifically, we introduce models with vorticity and present some new perspectives on the link between the Green-Kubo's formula and the hydrodynamics of non-gradient models.

arXiv commentarXiv admin note: text overlap with arXiv:1703.02418

References in corpus (6)

• Stochastic interacting particle systems out of equilibrium
• Large deviations for a stochastic model of heat flow
• Generalized inverses of Markovian kernels in terms of properties of the Markov chain
• Which random walks are cyclic?
• Gibbsian stationary non equilibrium states
• Totally asymmetric limit for models of heat conduction

Cited by in corpus (1)

• Hydrodynamic limit of an exclusion process with vorticity