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Dissipative electromagnetism from a nonequilibrium thermodynamics perspective.
Asja Jelić1, Markus Hütter, Hans Christian Ottinger
1Department of Materials, Institute of Polymers, ETH Zurich, 8093 Zurich, Switzerland.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
Summary
This study derives macroscopic electromagnetic dissipative effects from microscopic equations using Green-Kubo expressions. The findings are integrated into the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework.
Area of Science:
- Electromagnetism
- Statistical Mechanics
- Thermodynamics
Background:
- Macroscopic electromagnetic phenomena often exhibit dissipative effects.
- Microscopic Maxwell equations govern electromagnetic behavior.
- Bridging microscopic and macroscopic scales requires careful consideration of averaging and fluctuations.
Purpose of the Study:
- To derive dissipative effects in electromagnetism on macroscopic scales.
- To develop a method for connecting microscopic fluctuations to macroscopic dissipation.
- To formulate macroscopic Maxwell equations within a consistent thermodynamic framework.
Main Methods:
- Coarse-graining the microscopic Maxwell equations over time.
- Utilizing Green-Kubo type expressions relating dissipation to microscopic fluctuations and correlations.
- Employing the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework.
Main Results:
- A procedure for deriving macroscopic dissipative effects from microscopic electromagnetic equations is presented.
- The derived macroscopic Maxwell equations incorporate dissipative terms.
- The formulation is consistent with the GENERIC framework, allowing for inhomogeneous temperature considerations.
Conclusions:
- Dissipative effects in electromagnetism can be systematically derived from microscopic principles.
- The Green-Kubo approach provides a link between microscopic dynamics and macroscopic irreversibility.
- The GENERIC framework offers a robust foundation for describing macroscopic electromagnetic phenomena with dissipation and temperature gradients.
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