Untangling Dissipative and Hamiltonian effects in bulk and boundary driven systems

D. R. Michiel Renger; Upanshu Sharma

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arXiv · 2205.05327

Untangling Dissipative and Hamiltonian effects in bulk and boundary driven systems

D. R. Michiel Renger·Upanshu Sharma

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Abstract

Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behaviour of non-equilibrium dynamics and steady states in diffusive systems. We extend this framework to a minimal model of non-equilibrium non-diffusive system, specifically an open linear network on a finite graph. We explicitly calculate the dissipative bulk and boundary forces that drive the system towards the steady state, and non-dissipative bulk and boundary forces that drives the system in orbits around the steady state. Using the fact that these forces are orthogonal in a certain sense, we provide a decomposition of the large-deviation cost into dissipative and non-dissipative terms. We establish that the purely non-dissipative force turns the dynamics into a Hamiltonian system. These theoretical findings are illustrated by numerical examples.

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D. R. Michiel Renger, Upanshu Sharma. 2022-05-11. Untangling Dissipative and Hamiltonian effects in bulk and boundary driven systems. https://arxiv.org/abs/2205.05327

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