Related papers: Statistical and strict momentum conservation
In 2010 Menon and Srinivasan published a conjecture for the statistical structure of solutions $\rho$ to scalar conservation laws with certain Markov initial conditions, proposing a kinetic equation that should suffice to describe…
Transition rates in continuously driven steady states were derived in [Evans R M L, 2005 J. Phys. A: Math. Gen. 38, 293] by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
In this paper, we consider scalar conservation laws with smoothly varying spatially heterogeneous flux that is convex in the conserved variable. We show that under certain assumptions, a shock wave connecting two constant states emerges in…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
Magnetism primarily describes the physics and materials science of systems presenting a magnetization -- a macroscopic order parameter characterizing electron angular momentum. The order parameter is associated with the electronic exchange…
When dealing with macroscopic objects one usually observes quasiclassical phenomena, which can be described in terms of quasiclassical (or classical) equations of motion. Recent development of the theory of quantum computation is based on…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
Black holes can be practically located (e.g. in numerical simulations) by trapping horizons, hypersurfaces foliated by marginal surfaces, and one desires physically sound measures of their mass and angular momentum. A generically unique…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
This work describes underlying features of the universe such as fundamental constants and cosmological parameters, conservation laws, baryon and lepton asymmetries, etc. in the context of local gauge theories for fundamental forces under…
The balance of pseudomomentum is discussed and applied to simple elasticity, ideal fluids, and the mechanics of inextensible rods and sheets. A general framework is presented in which the simultaneous variation of an action with respect to…
The aim of this paper is to use large deviation theory in order to compute the entropy of macrostates for the microcanonical measure of the shallow water system. The main prediction of this full statistical mechanics computation is the…
Conservation of current and conservation of charge are nearly the same thing: when enough is known about charge movement, conservation of current can be derived from conservation of charge, in ideal dielectrics, for example. Conservation of…
The motion of one-hundred point vortices in a circular cylinder is simulated numerically and compared with theoretical predictions based on statistical mechanics. The novel aspect considered here is that the vortices have greatly different…
A system of identical disks is confined to a narrow channel, closed off at one end by a stopper and at the other end by a piston. All surfaces are hard and frictionless. A uniform gravitational field is directed parallel to the plane of the…
Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…
How the energy conservation law is obeyed by the universe during its evolution is an important but not yet unanimously resolved question. Does the universe have a constant mass during its evolution or has its mass been increasing with its…
Using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one…