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Abstract The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of probability measures, where paths are solutions of the continuity equation and the action is the kinetic energy. Here we consider a fundamental modification of the framework where the paths are solutions of nonlocal (jump) continuity equations and the action is a nonlocal kinetic energy. The resulting nonlocal Wasserstein distances are relevant to fractional diffusions and Wasserstein distances on graphs. We characterize the basic properties of the distance and obtain sharp conditions on the (jump) kernel specifying the nonlocal transport that determine whether the topology metrized is the weak or the strong topology. A key result of the paper are the quantitative comparisons between the nonlocal and local Wasserstein distance.
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Thermodynamic constraints on kinetic perturbations of homogeneous driven diffusions
Abstract We analyze the static response to kinetic perturbations of nonequilibrium steady states that can be modeled as diffusions. We demonstrate that kinetic response is purely a nonequilibirum effect, measuring the degree to which the Fluctuation-Dissipation Theorem is violated out of equilibrium. For driven diffusions in a flat landscape, we further demonstrate that such response is constrained by the strength of the nonequilibrium driving via quantitative inequalities.
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- Award ID(s):
- 2142466
- PAR ID:
- 10508573
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Europhysics Letters
- Volume:
- 146
- Issue:
- 3
- ISSN:
- 0295-5075
- Format(s):
- Medium: X Size: Article No. 31001
- Size(s):
- Article No. 31001
- Sponsoring Org:
- National Science Foundation
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