2,022 research outputs found
Gibbs Entropy and Irreversibility
This contribution is dedicated to dilucidating the role of the Gibbs entropy
in the discussion of the emergence of irreversibility in the macroscopic world
from the microscopic level. By using an extension of the Onsager theory to the
phase space we obtain a generalization of the Liouville equation describing the
evolution of the distribution vector in the form of a master equation. This
formalism leads in a natural way to the breaking of the BBGKY hierarchy. As a
particular case we derive the Boltzmann equation
Exact Results for the Asymmetric Simple Exclusion Process with a Blockage
We present new results for the current as a function of transmission rate in
the one dimensional totally asymmetric simple exclusion process (TASEP) with a
blockage that lowers the jump rate at one site from one to r < 1. Exact finite
volume results serve to bound the allowed values for the current in the
infinite system. This proves the existence of a gap in allowed density
corresponding to a nonequilibrium ``phase transition'' in the infinite system.
A series expansion in r, derived from the finite systems, is proven to be
asymptotic for all sufficiently large systems. Pade approximants based on this
series, which make specific assumptions about the nature of the singularity at
r = 1, match numerical data for the ``infinite'' system to a part in 10^4.Comment: 18 pages, LaTeX (including figures in LaTeX picture mode
On the uniqueness of Gibbs states in the Pirogov-Sinai theory
We prove that, for low-temperature systems considered in the Pirogov-Sinai
theory, uniqueness in the class of translation-periodic Gibbs states implies
global uniqueness, i.e. the absence of any non-periodic Gibbs state. The
approach to this infinite volume state is exponentially fast.Comment: 12 pages, Plain TeX, to appear in Communications in Mathematical
Physic
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