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Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
Standard results for the fluctuations of thermodynamic quantities are derived under the assumption of sampling identical systems that are in different, not fully equilibrated states. These results apply to fluctuations with time in a…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Multi-particle collision dynamics is an appealing numerical technique aiming at simulating fluids at the mesoscopic scale. It considers molecular details in a coarse-grained fashion and reproduces hydrodynamic phenomena. Here, the…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the…
Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single…
Extensive Monte Carlo simulations of bulk liquid para-hydrogen at a temperature T=16.5 K have been carried out using the continuous-space Worm Algorithm. Results for the momentum distribution, as well as for the kinetic energy per particle…
A roughly constant temperature over a wide range of densities is maintained in molecular clouds through radiative heating and cooling. An isothermal equation of state is therefore frequently employed in molecular cloud simulations. However,…
Classical molecular dynamics simulations of hydrogen plasmas have been performed with emphasis on the analysis of equilibration process. Theoretical basis of simulation model as well as numerically relevant aspects -- such as the proper…
Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational…
For more than 150 years the Navier-Stokes equations for thermodynamically quasi-equilibrium flows have been the cornerstone of modern computational fluid dynamics that underpins new fluid technologies. However, the applicable regime of the…
We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
We consider the Euler equation of quasi-geostrophic fluids which is widely used in weather forecast. Our goal is to study explicit volume-preserving numerical methods for very long simulations on an energy and enstrophy preserving…
Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…
We derive hydrodynamics of a prototypical one dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients - the hardcore…