Related papers: Continuum mechanics for the elastic properties of …
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and…
The macroscopic hydrodynamic equations are derived for many-body systems in the local-equilibrium approach, using the Schr\"odinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic…
Equilibrium properties in statistical physics are obtained by computing averages with respect to Boltzmann-Gibbs measures, sampled in practice using ergodic dynamics such as the Langevin dynamics. Some quantities however cannot be computed…
A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body rotational kinetic energy. The prototype…
Drag and diffusion of mobile ions in solids are of interest for both purely theoretical and applied scientific communities. This article proposes a theoretical description of ion drag in solids that can be used to estimate ionic…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to…
The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and non-equilibrium thermodynamics. The governing equations of irreversible…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal effects within a macroscopic continuum. The nonlocal…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
The hydrodynamics of thin films is typically described using phenomenological models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good…
We introduce a novel approach to model heat transport in solids, based on the Green-Kubo theory of linear response. It naturally bridges the Boltzmann kinetic approach in crystals and the Allen-Feldman model in glasses, leveraging…
We present a microscopic derivation of the nonlinear fluctuating hydrodynamic equation for the homogeneous crystalline solid from the Hamiltonian description of a many-particle system. We propose a microscopic expression of the displacement…
In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the…
A non-equilibrium steady state can be characterized by a nonzero but stationary flux driven by a static external force. Under a weak external force, the drift velocity is difficult to detect because the drift motion is feeble and submerged…
In this work a periodic crystal with point defects is described in the framework of linear response theory for broken symmetry states using correlation functions and Zwanzig-Mori equations. The main results are microscopic expressions for…