77,630 research outputs found
Orbital measures in non-equilibrium statistical mechanics: the Onsager relations
We assume that the properties of nonequilibrium stationary states of systems
of particles can be expressed in terms of weighted orbital measures, i.e.
through periodic orbit expansions. This allows us to derive the Onsager
relations for systems of particles subject to a Gaussian thermostat, under
the assumption that the entropy production rate is equal to the phase space
contraction rate. Moreover, this also allows us to prove that the relevant
transport coefficients are not negative. In the appendix we give an argument
for the proper way of treating grazing collisions, a source of possible
singularities in the dynamics.Comment: LaTeX, 14 pages, 1 TeX figure in the tex
Very Special Relativity
By Very Special Relativity (VSR) we mean descriptions of nature whose
space-time symmetries are certain proper subgroups of the Poincar\'e group.
These subgroups contain space-time translations together with at least a
2-parameter subgroup of the Lorentz group isomorphic to that generated by
and . We find that VSR implies special relativity
(SR) in the context of local quantum field theory or of CP conservation. Absent
both of these added hypotheses, VSR provides a simulacrum of SR for which most
of the consequences of Lorentz invariance remain wholly or essentially intact,
and for which many sensitive searches for departures from Lorentz invariance
must fail. Several feasible experiments are discussed for which
Lorentz-violating effects in VSR may be detectable.Comment: 3 pages, revte
Gibbs entropy and irreversible thermodynamics
Recently a number of approaches has been developed to connect the microscopic
dynamics of particle systems to the macroscopic properties of systems in
nonequilibrium stationary states, via the theory of dynamical systems. This way
a direct connection between dynamics and Irreversible Thermodynamics has been
claimed to have been found. However, the main quantity used in these studies is
a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its
present form, to characterize nonequilibrium states. Various simplified models
have also been devised to give explicit examples of how the coarse-grained
approach may succeed in giving a full description of the Irreversible
Thermodynamics. We analyze some of these models pointing out a number of
difficulties which, in our opinion, need to be overcome in order to establish a
physically relevant connection between these models and Irreversible
Thermodynamics.Comment: 19 pages, 4 eps figures, LaTeX2
A determinant formula for the Jones polynomial of pretzel knots
This paper presents an algorithm to construct a weighted adjacency matrix of
a plane bipartite graph obtained from a pretzel knot diagram. The determinant
of this matrix after evaluation is shown to be the Jones polynomial of the
pretzel knot by way of perfect matchings (or dimers) of this graph. The weights
are Tutte's activity letters that arise because the Jones polynomial is a
specialization of the signed version of the Tutte polynomial. The relationship
is formalized between the familiar spanning tree setting for the Tait graph and
the perfect matchings of the plane bipartite graph above. Evaluations of these
activity words are related to the chain complex for the Champanerkar-Kofman
spanning tree model of reduced Khovanov homology.Comment: 19 pages, 12 figures, 2 table
Note on Phase Space Contraction and Entropy Production in Thermostatted Hamiltonian Systems
The phase space contraction and the entropy production rates of Hamiltonian
systems in an external field, thermostatted to obtain a stationary state are
considered. While for stationary states with a constant kinetic energy the two
rates are formally equal for all numbers of particles N, for stationary states
with constant total (kinetic and potential) energy this only obtains for large
N. However, in both cases a large number of particles is required to obtain
equality with the entropy production rate of Irreversible Thermodynamics.
Consequences of this for the positivity of the transport coefficients and for
the Onsager relations are discussed. Numerical results are presented for the
special case of the Lorentz gas.Comment: 16 pages including 1 table and 3 figures. LaTeX forma
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