Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of field stochastic and quantum thermodynamics, ideas thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics statistics, optimal transport theory concerns by which one can optimally source distribution target distribution, deriving useful metric between probability distributions, called Wasserstein distance. Despite their seemingly unrelated nature, intimate connection these fields has unveiled context continuous-state Langevin dynamics, providing several important implications nonequilibrium this study, we elucidate analogous discrete cases developing thermodynamic framework transport. We first introduce novel quantity dynamical state mobility, significantly improves uncertainty relation provides insights into precision currents Markov jump processes. then derive variational formulas that connect distances Markovian dynamics described master equations. Specifically, rigorously prove distance equals minimum product irreversible entropy production mobility over all admissible dynamics. These not only unify relationship continuous cases, but also generalize it case. addition, demonstrate obtained lead remarkable applications such stringent speed limits finite-time Landauer principle. bounds are tight be saturated arbitrary temperatures, even zero-temperature limit. Notably, principle explain finite dissipation at extremely low cannot explained conventional principle.1 MoreReceived 26 July 2022Revised 1 December 2022Accepted 13 2022DOI:https://doi.org/10.1103/PhysRevX.13.011013Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further work must maintain attribution author(s) published article’s title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasEntropy productionNonequilibrium & thermodynamicsNonequilibrium statistical mechanicsQuantum thermodynamicsStochastic processesStochastic thermodynamicsThermodynamics computationTechniquesGraph theoryStatistical PhysicsInterdisciplinary PhysicsGeneral Physics