Soluble Model of a Nonequilibrium Steady State: The Van Kampen Objection and Other Lessons
Abstract
A simple model of charge transport is provided by a classical particle in a random potential and a dissipative coupling to the environment. The corresponding nonequilibrium steady state (NESS) can be determined analytically when both the disorder and dissipation are weak. We use it to illuminate some foundational issues in nonequilibrium statistical mechanics. We show that at nonlinear level dissipative response sensitively depends on the system-environment coupling, and the range of validity of the linear response theory is set by this coupling. This validates the Van Kampen objection. We also show that the principle of minimum entropy production does not determine the NESS beyond linear order in the electric field, while entropy maximization fails to produce the correct NESS already at linear order.
Copyright and License
© 2024 American Physical Society.
Acknowledgement
The author would like to thank Gregory Falkovich and Boris Spivak for numerous illuminating discussions and to the Weizmann Institute of Science for hospitality. This work was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632 and by the Simons Investigator Award.
Supplemental Material
The supplemental material contains a derivation of the Fokker-Planck equation. The derivation is a slight generalization of an existing one in the literature (Ref. 13) to account for a weak dissipation.
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Additional details
- United States Department of Energy
- DE-SC0011632
- Simons Investigator Award
- Accepted
-
2024-09-12Accepted
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Publication Status
- Published