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Untangling dissipative and Hamiltonian effects in bulk and boundary-driven systems.
D R Michiel Renger1, Upanshu Sharma2
1Department of Mathematics, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany.
Physical Review. E
|December 20, 2023
Summary
Macroscopic fluctuation theory is extended to nondiffusive systems, revealing how forces drive steady states and orbits. This work decomposes large-deviation costs and shows nondissipative forces create Hamiltonian systems.
Area of Science:
- Non-equilibrium statistical mechanics
- Theoretical physics
- Complex systems
Background:
- Macroscopic fluctuation theory (MFT) analyzes nonequilibrium dynamics in diffusive systems.
- Understanding nondiffusive systems requires extending existing theoretical frameworks.
- Large deviation theory is crucial for characterizing rare events in stochastic systems.
Purpose of the Study:
- To extend Macroscopic Fluctuation Theory (MFT) to a minimal nonequilibrium nondiffusive system.
- To analyze the role of dissipative and nondissipative forces in driving system dynamics.
- To decompose the large-deviation cost and investigate the emergence of Hamiltonian dynamics.
Main Methods:
- Application of large deviation theory to an open linear network on a finite graph.
- Explicit calculation of bulk and boundary forces (dissipative and nondissipative).
- Decomposition of the large-deviation cost based on the orthogonality of forces.
Main Results:
- Identification and calculation of dissipative forces driving the system to a steady state.
- Identification and calculation of nondissipative forces causing orbits around the steady state.
- Demonstration that purely nondissipative forces result in Hamiltonian dynamics.
- Decomposition of large-deviation cost into dissipative and nondissipative components.
Conclusions:
- The extended MFT framework successfully analyzes nonequilibrium nondiffusive systems.
- The interplay between dissipative and nondissipative forces is key to understanding system behavior.
- The emergence of Hamiltonian dynamics from nondissipative forces offers new insights into complex systems.
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