WIAS Preprint No. 2936, (2022)

Untangling dissipative and Hamiltonian effects in bulk and boundary driven systems


  • Renger, D. R. Michiel
    ORCID: 0000-0003-3557-3485
  • Sharma, Upanshu

2020 Mathematics Subject Classification

  • 05C21 49S05 60F10 60J27 82C35


  • Open graphs, non-equilibrium thermodynamics, macroscopic fluctuation theory


Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behaviour of non-equilibrium dynamics and steady states in emphdiffusive systems. We extend this framework to a minimal model of non-equilibrium emphnon-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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