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Published on: December 4, 2017
Generalized Green-Kubo relation and integral fluctuation theorem for driven dissipative systems without microscopic
Song-Ho Chong1, Michio Otsuki, Hisao Hayakawa
1Institute for Molecular Science, Okazaki 444-8585, Japan.
Summary
We developed new statistical mechanics theories for driven dissipative systems, extending the Green-Kubo relation and fluctuation theorem. This work addresses systems far from equilibrium, like sheared granular materials.
Area of Science:
- Statistical mechanics
- Non-equilibrium thermodynamics
- Complex systems
Background:
- Traditional statistical mechanics often assumes equilibrium or near-equilibrium conditions.
- Driven dissipative systems, characterized by broken time-reversal symmetry, pose challenges for existing theories.
- Understanding non-equilibrium steady states is crucial for many physical phenomena.
Purpose of the Study:
- To derive a generalized Green-Kubo relation applicable to driven dissipative systems.
- To formulate an integral form of the fluctuation theorem for systems with broken detailed balance.
- To establish a framework for statistical mechanical theories of non-equilibrium steady states.
Main Methods:
- Derivation of generalized Green-Kubo relations.
- Formulation of an integral fluctuation theorem.
- Application to specific models: uniformly sheared granular systems and driven inelastic Lorentz gas.
Main Results:
- Successfully derived generalized Green-Kubo and fluctuation relations for driven dissipative systems.
- Demonstrated the applicability of these relations to granular materials and Lorentz gas models.
- Provided a pathway for constructing statistical mechanical theories for systems lacking equilibrium.
Conclusions:
- The derived relations offer powerful tools for analyzing non-equilibrium steady states.
- These findings advance the statistical mechanical understanding of systems far from equilibrium.
- The theoretical framework is applicable to a range of complex, driven systems.
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