Thermodynamic interpretation of Wasserstein distance

Abstract

We derive a relation between the dissipation in a stochastic dynamics and the Wasserstein distance. We show that the minimal amount of dissipation required to transform an initial state to a final state during a diffusion process is given by the Wasserstein distance between the two states, divided by the total time of the process. This relation implies a lower bound on the dissipation for any diffusion process in terms of its initial and final state. Using a lower bound on the Wasserstein distance, we further show that we can give a lower bound on the dissipation in terms of only the mean and convariance matrix of the initial and final state. We apply this result to derive the optimal forces that minimize the dissipation for given initial and final mean and covariance.

arXiv comment5 pages

References in corpus (15)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Speed Limit for Classical Stochastic Processes
• Optimal protocols and optimal transport in stochastic thermodynamics
• Finite-time generalization of the thermodynamic uncertainty relation
• Refined Second Law of Thermodynamics for fast random processes
• Current fluctuations and transport efficiency for general Langevin systems
• Quantum Speed Limit is Not Quantum
• Entropy production in full phase space for continuous stochastic dynamics
• Entropic bounds on currents in Langevin systems
• Optimal performance of periodically driven, stochastic heat engines under limited control

Cited by in corpus (15)

• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Finite-time Landauer principle
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes
• Optimal finite-time bit erasure under full control
• Geometric decomposition of entropy production into excess, housekeeping and coupling parts
• Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems
• Optimality of non-conservative driving for finite-time processes with discrete states
• Thermodynamic speed limits for mechanical work
• Optimal finite-time heat engines under constrained control
• Wasserstein distance in speed limit inequalities for Markov jump processes
• Maximal power output of a stochastic thermodynamic engine
• Evading Thermodynamic Uncertainty Relations via Asymmetric Dynamic Protocols
• Relations between entropy rate, entropy production and information geometry in linear stochastic systems