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A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The…
Sampling Gibbs measures at low temperatures is an important task but computationally challenging. Numerical evidence suggests that the infinite-swapping algorithm (isa) is a promising method. The isa can be seen as an improvement of the…
The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the…
We present the complete set of stochastic Verlet-type algorithms that can provide correct statistical measures for both configurational and kinetic sampling in discrete-time Langevin systems. The approach is a brute-force general…
In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…
In light of the recently published complete set of statistically correct Gronbech-Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the…
We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. We start by noticing the equivalence of their description through the…
We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath. We apply the formalism to clarify issues of principle regarding the sources and signatures of…
We study numerical methods for the generalized Langevin equation (GLE) with a positive Prony series memory kernel, in which case the GLE can be written in an extended variable Markovian formalism. We propose a new splitting method that is…
We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
We show how to derive a simple integrator for the Langevin equation and illustrate how it is possible to check the accuracy of the obtained distribution on the fly, using the concept of effective energy introduced in a recent paper [J.…
A new method is presented for performing first-principles molecular-dynamics simulations of systems with variable occupancies. We adopt a matrix representation for the one-particle statistical operator Gamma, to introduce a ``projected''…
We numerically investigate stochastic dynamics in cosmology by solving Langevin equations for Infrared (IR) modes with stochastic noises generated by Ultraviolet (UV) modes at the coarse-graining scale. By construction, the stochastic…
We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and…
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…
The energetic optimization problem, e.g., searching for the optimal switch- ing protocol of certain system parameters to minimize the input work, has been extensively studied by stochastic thermodynamics. In current work, we study this…
We revisit the modeling framework introduced in [N. Loy and L. Preziosi: Bull. Math. Bio., 85, 2023] to describe the dynamics of cell orientation under cyclic stretch. We propose a reformulation based on the principles of Stochastic…
A novel mixed quantum-classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees…
In complex systems with many degrees of freedom such as peptides and proteins there exist a huge number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped…