Related papers: Irreversibility in the short memory approximation
Over the past few decades, a host of theoretical evidence have surfaced that suggest a connection between theories of gravity and Navier-Stokes (NS) equation of fluid dynamics. It emerges out that gravity theory can be treated as some kind…
A careful derivation of the generalized Langevin equation using "Zwanzig flavor" projection operator formalism is presented. We provide arguments why this formalism has better properties compared to alternative projection-operator…
We present a framework, which, from the trajectories detailing the spatiotemporal dynamics of a population, simultaneously reconstructs a transport map as well as the Fokker-Planck equation governing the coarse-grained probability…
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous…
We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains.…
Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is…
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…
Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master Equation that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…
Equations of motion for the microscopic number density $\hat{\rho}({\bf x},t)$ and the momentum density $\hat{\bf g}({\bf x},t)$ of a fluid have been obtained in the past from the corresponding Langevin equations representing the dynamics…
The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully…
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…
This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear…
A novel algorithm for the direct numerical simulation of the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser (1987) for incompressible flow is presented here. A Fourier representation is…
We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…
Second-order relativistic hydrodynamics is surprisingly predictive, even in the presence of large gradients. The hydrodynamic expansion from the method of moments does not require a gradient expansion, but it is intrinsically bound to the…
In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted…
To close the moment model deduced from kinetic equations, the canonical approach is to provide an approximation to the flux function not able to be depicted by the moments in the reduced model. In this paper, we propose a brand new closure…