Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance

We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. show that lower bound on entropy production is action measured by path length of $L^2$-Wasserstein distance. Because distance geometric measure theory, our result implies interpretation production. Based this interpretation, we obtain thermodynamic trade-off relation transition time This regarded as speed limit which gives tighter also discuss subsystem derive partial generalization second law information thermodynamics. Our formalism provides picture protocol to minimize illustrate these results heat engine geometrical efficiency.