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

@article{Nakazato2021GeometricalAO,
  title={Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance},
  author={Muka Nakazato and Sousuke Ito},
  journal={Physical Review Research},
  year={2021}
}
We study a relationship between optimal transport theory and stochastic thermodynamics for the FokkerPlanck equation. We show that the lower bound on the entropy production is the action measured by the path length of the L-Wasserstein distance. Because the L-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off between transition time and… 

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