This paper writes the three-wave and four-wave kinetic equations as GENERIC thermodynamic systems and formally derives a Landau-type small-angle limit for the four-wave equation, with a GENERIC structure for the limiting system.
GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles
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abstract
In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (\"Ottinger 2005). This interpretation provides (a) a variational formulation for GENERIC systems, (b) insight into the origin of this variational formulation, and (c) an explanation of the origins of the conditions that GENERIC places on its constitutive elements, notably the so-called degeneracy or non-interaction conditions. This work shows how the general connection between large-deviation principles on one hand and gradient-flow structures on the other hand extends to non-reversible particle systems.
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GENERIC formulation and small-angle limit for Kinetic wave equations
This paper writes the three-wave and four-wave kinetic equations as GENERIC thermodynamic systems and formally derives a Landau-type small-angle limit for the four-wave equation, with a GENERIC structure for the limiting system.