Finite-time driving of stochastic systems generates excess dissipation, causing the evolving probability distribution to lag behind the instantaneous equilibrium, and consequently degrading the convergence of nonequilibrium free energy estimators based on the Jarzynski equality. Escorted free energy simulations address the non-adiabatic lag by engineering control fields $\mathbf{u}$ that eliminate the lag, enforcing the trajectory-wise equality $\mathcal{W}_\mathbf{u} = Δ\mathcal{F}$, and yielding zero-variance estimators.
arXiv:2606. 08343v1 Announce Type: new Abstract: We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space.
By Jason Sulskis, Sathya Ravi
arXiv:2510. 22778v3 Announce Type: replace-cross Abstract: We develop a free-probabilistic framework for denoising diffusion, in which the data is a self-adjoint operator and its law a spectral distribution.
By Swagatam Das
arXiv:2607. 16281v1 Announce Type: cross Abstract: The analysis of highly non-linear stochastic data within non-equilibrium dynamical systems requires computational frameworks capable of detecting latent phase transitions before systemic structural breakdowns occur.
By Manoj B. Bhatkar, Prashant M. Yawalkar
arXiv:2606. 21828v2 Announce Type: replace-cross Abstract: Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction.
By Jaemin Oh, Youngkyu Lee, Jerome Darbon, George Em Karniadakis
Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $σ_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $σ_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $σ_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $σ_{\min}$-uniform coefficients, computable on a pretrained checkpoint without ground-truth scores or exact trajectories.
arXiv:2607. 13022v1 Announce Type: cross Abstract: Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state.
By Gianluca Galletti, Gerald Gutenbrunner, William Hornsby, Lorenzo Zanisi, Naomi Carey, Stanislas Pamela, Johannes Brandstetter, Fabian Paischer
arXiv:2607. 04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer.
By Shiheng Zhang
arXiv:2607. 24741v2 Announce Type: replace-cross Abstract: Positive two-marginal entropic optimal transport is solved by a nonlinear, positive, order-preserving, homogeneous Sinkhorn map.
By Xinyang Wen
arXiv:2605. 27478v3 Announce Type: replace-cross Abstract: Schr\"odinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid.
By Gabriele Bocchi
arXiv:2606. 28808v1 Announce Type: cross Abstract: We study the leading-order fluctuation of stochastic gradient Euler-Maruyama estimators for generalized non-reversible Langevin dynamics.
By Bingye Ni, Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
arXiv:2606. 30687v1 Announce Type: cross Abstract: Diffusion models are increasingly utilized for modeling molecular structures and conformational ensembles, yet the thermodynamic meaning of their learned representations and scores remains elusive.
By Wenjie Xi