20,881 research outputs found
Minimum Dissipation Principle in Nonlinear Transport
We extend Onsager's minimum dissipation principle to stationary states that
are only subject to local equilibrium constraints, even when the transport
coefficients depend on the thermodynamic forces. Crucial to this generalization
is a decomposition of the thermodynamic forces into those that are held fixed
by the boundary conditions, and the subspace which is orthogonal with respect
to the metric defined by the transport coefficients. We are then able to apply
Onsager and Machlup's proof to the second set of forces. As an example we
consider two-dimensional nonlinear diffusion coupled to two reservoirs at
different temperatures. Our extension differs from that of Bertini et al. in
that we assume microscopic irreversibility and we allow a nonlinear dependence
of the fluxes on the forces.Comment: 20 pages, 1 figur
On the physical implications of Hawking's spacetime foam
Hawking's spacetime foam model predicts that due to quantum fluctuations,
spacetime is filled with black hole like objects. We argue that Hawking's model
implies a cosmological constant of the observed order and that it can also be
used to solve the problem of time in quantum gravity.Comment: 12 page
A Fully Self-Consistent Treatment of Collective Fluctuations in Quantum Liquids
The problem of calculating collective density fluctuations in quantum liquids
is revisited. A fully quantum mechanical self-consistent treatment based on a
quantum mode-coupling theory [E. Rabani and D.R. Reichman, J. Chem. Phys.116,
6271 (2002)] is presented. The theory is compared with the maximum entropy
analytic continuation approach and with available experimental results. The
quantum mode-coupling theory provides semi-quantitative results for both short
and long time dynamics. The proper description of long time phenomena is
important in future study of problems related to the physics of glassy quantum
systems, and to the study of collective fluctuations in Bose fluids.Comment: 9 pages, 4 figure
Improving Christofides' Algorithm for the s-t Path TSP
We present a deterministic (1+sqrt(5))/2-approximation algorithm for the s-t
path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices
including two prespecified endpoints, the problem is to find a shortest
Hamiltonian path between the two endpoints; Hoogeveen showed that the natural
variant of Christofides' algorithm is a 5/3-approximation algorithm for this
problem, and this asymptotically tight bound in fact has been the best
approximation ratio known until now. We modify this algorithm so that it
chooses the initial spanning tree based on an optimal solution to the Held-Karp
relaxation rather than a minimum spanning tree; we prove this simple but
crucial modification leads to an improved approximation ratio, surpassing the
20-year-old barrier set by the natural Christofides' algorithm variant. Our
algorithm also proves an upper bound of (1+sqrt(5))/2 on the integrality gap of
the path-variant Held-Karp relaxation. The techniques devised in this paper can
be applied to other optimization problems as well: these applications include
improved approximation algorithms and improved LP integrality gap upper bounds
for the prize-collecting s-t path problem and the unit-weight graphical metric
s-t path TSP.Comment: 31 pages, 5 figure
Time Evolution In Macroscopic Systems. II: The Entropy
The concept of entropy in nonequilibrium macroscopic systems is investigated
in the light of an extended equation of motion for the density matrix obtained
in a previous study. It is found that a time-dependent information entropy can
be defined unambiguously, but it is the time derivative or entropy production
that governs ongoing processes in these systems. The differences in physical
interpretation and thermodynamic role of entropy in equilibrium and
nonequilibrium systems is emphasized and the observable aspects of entropy
production are noted. A basis for nonequilibrium thermodynamics is also
outlinedComment: 28 page
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