Related papers: Error Analysis of Modified Langevin Dynamics
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
Bayesian inference allows to obtain useful information on the parameters of models, either in computational statistics or more recently in the context of Bayesian Neural Networks. The computational cost of usual Monte Carlo methods for…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…
The recently discovered supersymmetric generalizations of Langevin dynamics and Kramers equation can be utilized for the exploration of free energy landscapes of systems whose large time-scale separation hampers the usefulness of standard…
The advantages of performing Langevin Dynamics in extended systems are discussed. A simple Langevin Dynamics scheme for producing the canonical ensemble is reviewed, and is then extended to the Hoover ensemble. We show that the resulting…
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…
Low energy nucleon dynamics is investigated by using the generalized dynamical equation derived in [J. Phys. A v.32, 5657 (1999)]. This equation extends quantum dynamics to describe the time evolution in the case of nonlocal-in-time…
Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion [1,2,3].…
We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in…
We develop a way of improving complex Langevin dynamics motivated by the Lefschetz-thimble decomposition of integrals. In our method, arbitrary observables of an original model with multiple Lefschetz thimbles are computed by a modified…
We consider the thermodynamic potential describing the macroscopic fluctuation of the current and local energy of a general class of Hamiltonian models including aerogels. We argue that this potential is neither analytic nor strictly…
Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an "effective thermal equilibrium"…
Biological, artificial, and physical systems dissipate energy to accurately transmit information. While tools of information theory have been used to characterize information-processing capabilities, how reliably this information is…
Single particle tracking has become a standard tool to investigate diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual…
We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…
Using the recently developed covariant Ito-Langevin dynamics, we develop a non-equilibrium thermodynamic theory for small systems coupled to multiplicative noises. The theory is based on Ito-calculus, and is fully covariant under…
In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared to sampling from a time-reversible one. Adding…