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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.12285 |
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| _version_ | 1866910268320120832 |
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| author | Farmer, Michael Kochar, Abhinav Lee, Yugyung |
| author_facet | Farmer, Michael Kochar, Abhinav Lee, Yugyung |
| contents | We study transient nonequilibrium dynamics in Fisher-regularized Wasserstein gradient flows and identify a sign-changing cross-dissipation mechanism generated by the coupling between transport dissipation and Fisher-information geometry. Using the Ornstein--Uhlenbeck Fokker--Planck system as an analytically tractable setting, we derive an exact reduced variance dynamics on the Gaussian manifold, \[ \dot{u}=2(1-u)+\frac{\varepsilon}{u}, \] where \(u(t)=σ^2(t)\) is the variance and \(\varepsilon>0\) is the Fisher regularization strength. The reduced dynamics reveal distinct transient regimes induced by the interaction between transport relaxation and information-geometric curvature. The associated cross-dissipation term changes sign at the critical scale \(σ=1\), separating cooperative acceleration for localized states with \(σ<1\) from transient interference at larger variance scales. In the subcritical regime, Fisher curvature accelerates the descent of the baseline free energy; beyond the critical transition, it partially opposes the Ornstein--Uhlenbeck pullback and generates transient overshoot toward a displaced Fisher-regularized equilibrium. We also establish a bounded transient-acceleration-window result, showing that the cooperative acceleration phase has finite duration with an upper bound depending only on the Fisher regularization strength. Finite-difference simulations support the analytical predictions and suggest that qualitatively similar sign-transition behavior may persist beyond Gaussian closure for non-Gaussian initial conditions, including bimodal and Laplace distributions. Overall, the results provide a transient dynamical perspective on Fisher-regularized dissipative systems and show how information-geometric curvature can reorganize intermediate-time Wasserstein relaxation while preserving the globally dissipative structure of the flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transient Acceleration and Cross-Dissipation Interference in Fisher-Regularized Wasserstein Gradient Flows Farmer, Michael Kochar, Abhinav Lee, Yugyung Statistical Mechanics Information Theory Probability G.3, I.6.8 G.3; F.2.2 We study transient nonequilibrium dynamics in Fisher-regularized Wasserstein gradient flows and identify a sign-changing cross-dissipation mechanism generated by the coupling between transport dissipation and Fisher-information geometry. Using the Ornstein--Uhlenbeck Fokker--Planck system as an analytically tractable setting, we derive an exact reduced variance dynamics on the Gaussian manifold, \[ \dot{u}=2(1-u)+\frac{\varepsilon}{u}, \] where \(u(t)=σ^2(t)\) is the variance and \(\varepsilon>0\) is the Fisher regularization strength. The reduced dynamics reveal distinct transient regimes induced by the interaction between transport relaxation and information-geometric curvature. The associated cross-dissipation term changes sign at the critical scale \(σ=1\), separating cooperative acceleration for localized states with \(σ<1\) from transient interference at larger variance scales. In the subcritical regime, Fisher curvature accelerates the descent of the baseline free energy; beyond the critical transition, it partially opposes the Ornstein--Uhlenbeck pullback and generates transient overshoot toward a displaced Fisher-regularized equilibrium. We also establish a bounded transient-acceleration-window result, showing that the cooperative acceleration phase has finite duration with an upper bound depending only on the Fisher regularization strength. Finite-difference simulations support the analytical predictions and suggest that qualitatively similar sign-transition behavior may persist beyond Gaussian closure for non-Gaussian initial conditions, including bimodal and Laplace distributions. Overall, the results provide a transient dynamical perspective on Fisher-regularized dissipative systems and show how information-geometric curvature can reorganize intermediate-time Wasserstein relaxation while preserving the globally dissipative structure of the flow. |
| title | Transient Acceleration and Cross-Dissipation Interference in Fisher-Regularized Wasserstein Gradient Flows |
| topic | Statistical Mechanics Information Theory Probability G.3, I.6.8 G.3; F.2.2 |
| url | https://arxiv.org/abs/2603.12285 |