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L$^2$-Hypocoercivity for non-equilibrium kinetic equations
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abstract
The recent work [11] developed a general framework to show hypocoercivity for a stationary Gibbs state and allowed spatial degeneracy, confining potentials and boundary conditions. In this work, we show that the explicit energy approach in the weighted L$^2$ space works for general non-equilibrium steady states and that it can be adapted to cases with weaker confinement leading to algebraic decay.
Forward citations
Cited by 3 Pith papers
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Exponential Ergodicity in Relative Entropy and $L^2$-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs
Non-equilibrium kinetic SDEs under partial dissipation are shown to satisfy exponential ergodicity in relative entropy and L2-Wasserstein distance, with extensions to McKean-Vlasov and mean-field particle systems.
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L2 geometric ergodicity for the kinetic Langevin process with non-equilibrium steady states
A note showing that under a dissipativity-at-large-distance condition, the law of a non-equilibrium kinetic Langevin process converges to its steady state in L2 with rate exp(-c min(t,t^3)).
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Hypocoercivity meets lifts
A unified hypocoercivity framework shows adaptive Langevin dynamics is a near-optimal lift, and proves the generalized Langevin equation cannot beat square-root speedup.
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