139,297 research outputs found
Boosted Statistical Mechanics
Based on the fundamental principles of Relativistic Quantum Mechanics, we
give a rigorous, but completely elementary, proof of the relation between
fundamental observables of a statistical system when measured relatively to two
inertial reference frames, connected by a Lorentz transformation.Comment: 8 page
Hamiltonian statistical mechanics
A framework for statistical-mechanical analysis of quantum Hamiltonians is
introduced. The approach is based upon a gradient flow equation in the space of
Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve
toward those of the reference Hamiltonian. The nonlinear double-bracket
equation governing the flow is such that the eigenvalues of the initial
Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by
compact invariant subspaces, which permits the construction of statistical
distributions over the Hamiltonians. In two dimensions, an explicit dynamical
model is introduced, wherein the density function on the space of Hamiltonians
approaches an equilibrium state characterised by the canonical ensemble. This
is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde
Equilibrium Statistical Mechanics
An introductory review of Classical Statistical MechanicsComment: 56 page
Semiclassical Statistical Mechanics
We use a semiclassical approximation to derive the partition function for an
arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we
view as an example of finite temperature scalar Field Theory at a point. We
rely on Catastrophe Theory to analyze the pattern of extrema of the
corresponding path-integral. We exhibit the propagator in the background of the
different extrema and use it to compute the fluctuation determinant and to
develop a (nonperturbative) semiclassical expansion which allows for the
calculation of correlation functions. We discuss the examples of the single and
double-well quartic anharmonic oscillators, and the implications of our results
for higher dimensions.Comment: Invited talk at the La Plata meeting on `Trends in Theoretical
Physics', La Plata, April, 1997; 14 pages + 5 ps figures. Some cosmetical
modifications, and addition of some references which were missing in the
previous versio
Statistical mechanics of voting
Decision procedures aggregating the preferences of multiple agents can
produce cycles and hence outcomes which have been described heuristically as
`chaotic'. We make this description precise by constructing an explicit
dynamical system from the agents' preferences and a voting rule. The dynamics
form a one dimensional statistical mechanics model; this suggests the use of
the topological entropy to quantify the complexity of the system. We formulate
natural political/social questions about the expected complexity of a voting
rule and degree of cohesion/diversity among agents in terms of random matrix
models---ensembles of statistical mechanics models---and compute quantitative
answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages
General relativistic statistical mechanics
Understanding thermodynamics and statistical mechanics in the full general
relativistic context is an open problem. I give tentative definitions of
equilibrium state, mean values, mean geometry, entropy and temperature, which
reduce to the conventional ones in the non-relativistic limit, but remain valid
for a general covariant theory. The formalism extends to quantum theory. The
construction builds on the idea of thermal time, on a notion of locality for
this time, and on the distinction between global and local temperature. The
last is the temperature measured by a local thermometer, and is given by kT =
hbar d tau/ds, with k the Boltzmann constant, hbar the Planck constant, ds
proper time and d tau the equilibrium thermal time.Comment: A tentative second step in the thermal time direction, 10 years after
the paper with Connes. The aim is the full thermodynamics of gravity. The
language of the paper is a bit technical: look at the Appendix first
(expanded in version 2
Statistical mechanics of money
In a closed economic system, money is conserved. Thus, by analogy with
energy, the equilibrium probability distribution of money must follow the
exponential Gibbs law characterized by an effective temperature equal to the
average amount of money per economic agent. We demonstrate how the Gibbs
distribution emerges in computer simulations of economic models. Then we
consider a thermal machine, in which the difference of temperatures allows one
to extract a monetary profit. We also discuss the role of debt, and models with
broken time-reversal symmetry for which the Gibbs law does not hold.Comment: 7 pages, 5 figures, RevTeX. V.4: final version accepted to Eur. Phys.
J. B: few stylistic revisions and additional reference
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