1,817 research outputs found
On time's arrow in Ehrenfest models with reversible deterministic dynamics
We introduce a deterministic, time-reversible version of the Ehrenfest urn
model. The distribution of first-passage times from equilibrium to
non-equilibrium states and vice versa is calculated. We find that average times
for transition to non-equilibrium always scale exponentially with the system
size, whereas the time scale for relaxation to equilibrium depends on
microscopic dynamics. To illustrate this, we also look at deterministic and
stochastic versions of the Ehrenfest model with a distribution of microscopic
relaxation times.Comment: 6 pages, 7 figures, revte
Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations
We study the evolution of a two component fluid consisting of ``blue'' and
``red'' particles which interact via strong short range (hard core) and weak
long range pair potentials. At low temperatures the equilibrium state of the
system is one in which there are two coexisting phases. Under suitable choices
of space-time scalings and system parameters we first obtain (formally) a
mesoscopic kinetic Vlasov-Boltzmann equation for the one particle position and
velocity distribution functions, appropriate for a description of the phase
segregation kinetics in this system. Further scalings then yield Vlasov-Euler
and incompressible Vlasov-Navier-Stokes equations. We also obtain, via the
usual truncation of the Chapman-Enskog expansion, compressible
Vlasov-Navier-Stokes equations.Comment: TeX, 50 page
Self-Diffusion in Simple Models: Systems with Long-Range Jumps
We review some exact results for the motion of a tagged particle in simple
models. Then, we study the density dependence of the self diffusion
coefficient, , in lattice systems with simple symmetric exclusion in
which the particles can jump, with equal rates, to a set of neighboring
sites. We obtain positive upper and lower bounds on
for .
Computer simulations for the square, triangular and one dimensional lattice
suggest that becomes effectively independent of for .Comment: 24 pages, in TeX, 1 figure, e-mail addresses: [email protected],
[email protected], [email protected]
Cluster expansion in the canonical ensemble
We consider a system of particles confined in a box \La\subset\R^d
interacting via a tempered and stable pair potential. We prove the validity of
the cluster expansion for the canonical partition function in the high
temperature - low density regime. The convergence is uniform in the volume and
in the thermodynamic limit it reproduces Mayer's virial expansion providing an
alternative and more direct derivation which avoids the deep combinatorial
issues present in the original proof
Entropy of Open Lattice Systems
We investigate the behavior of the Gibbs-Shannon entropy of the stationary
nonequilibrium measure describing a one-dimensional lattice gas, of L sites,
with symmetric exclusion dynamics and in contact with particle reservoirs at
different densities. In the hydrodynamic scaling limit, L to infinity, the
leading order (O(L)) behavior of this entropy has been shown by Bahadoran to be
that of a product measure corresponding to strict local equilibrium; we compute
the first correction, which is O(1). The computation uses a formal expansion of
the entropy in terms of truncated correlation functions; for this system the
k-th such correlation is shown to be O(L^{-k+1}). This entropy correction
depends only on the scaled truncated pair correlation, which describes the
covariance of the density field. It coincides, in the large L limit, with the
corresponding correction obtained from a Gaussian measure with the same
covariance.Comment: Latex, 28 pages, 4 figures as eps file
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