2021/05/25 by Bertram Tschiderer, Tschiderer, Bertram, Lane Chun Yeung +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #60G44 #94A17 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Model Reduction and Neural Networks #Primary 60H30 #Probability (math.PR) #Statistical Mechanics and Entropy #secondary 60J60
paper · pdf · doi:10.48550/arxiv.2105.12248
openalex publication_date 2021/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate a trajectorial version of the relative entropy dissipation\nidentity for McKean-Vlasov diffusions, extending the results of the papers\n[FJ16,KST20a], which apply to non-interacting diffusions. Our stochastic\nanalysis approach is based on time-reversal of diffusions and Lions'\ndifferential calculus over Wasserstein space. It allows us to compute\nexplicitly the rate of relative entropy dissipation along every trajectory of\nthe underlying diffusion via the semimartingale decomposition of the\ncorresponding relative entropy process. As a first application, we obtain a new\ninterpretation of the gradient flow structure for the granular media equation,\ngeneralizing the formulation in [KST20a] developed for the linear\nFokker-Planck equation. Secondly, we show how the trajectorial approach leads\nto a new derivation of the HWBI inequality, which relates relative entropy (H),\nWasserstein distance (W), barycenter (B) and Fisher information (I).\n