1,038 research outputs found
Information in statistical physics
We review with a tutorial scope the information theory foundations of quantum
statistical physics. Only a small proportion of the variables that characterize
a system at the microscopic scale can be controlled, for both practical and
theoretical reasons, and a probabilistic description involving the observers is
required. The criterion of maximum von Neumann entropy is then used for making
reasonable inferences. It means that no spurious information is introduced
besides the known data. Its outcomes can be given a direct justification based
on the principle of indifference of Laplace. We introduce the concept of
relevant entropy associated with some set of relevant variables; it
characterizes the information that is missing at the microscopic level when
only these variables are known. For equilibrium problems, the relevant
variables are the conserved ones, and the Second Law is recovered as a second
step of the inference process. For non-equilibrium problems, the increase of
the relevant entropy expresses an irretrievable loss of information from the
relevant variables towards the irrelevant ones. Two examples illustrate the
flexibility of the choice of relevant variables and the multiplicity of the
associated entropies: the thermodynamic entropy (satisfying the Clausius-Duhem
inequality) and the Boltzmann entropy (satisfying the H-theorem). The
identification of entropy with missing information is also supported by the
paradox of Maxwell's demon. Spin-echo experiments show that irreversibility
itself is not an absolute concept: use of hidden information may overcome the
arrow of time.Comment: latex InfoStatPhys-unix.tex, 3 files, 2 figures, 32 pages
http://www-spht.cea.fr/articles/T04/18
Incomplete descriptions and relevant entropies
Statistical mechanics relies on the complete though probabilistic description
of a system in terms of all the microscopic variables. Its object is to derive
therefrom static and dynamic properties involving some reduced set of
variables. The elimination of the irrelevant variables is guided by the maximum
entropy criterion, which produces the probability law carrying the least amount
of information compatible with the relevant variables. This defines relevant
entropies which measure the missing information (the disorder) associated with
the sole variables retained in an incomplete description. Relevant entropies
depend not only on the state of the system but also on the coarseness of its
reduced description. Their use sheds light on questions such as the Second Law,
both in equilibrium an in irreversible thermodynamics, the projection method of
statistical mechanics, Boltzmann's \textit{H}-theorem or spin-echo experiment.Comment: flatex relevant_entropies.tex, 1 file Submitted to: Am. J. Phy
Stars and statistical physics: a teaching experience
The physics of stars, their workings and their evolution, is a goldmine of
problems in statistical mechanics and thermodynamics. We discuss many examples
that illustrate the possibility of deepening student's knowledge of statistical
mechanics by an introductory study of stars. The matter constituting the
various stellar objects provides examples of equations of state for classical
or quantal and relativistic or non-relativistic gases. Maximum entropy can be
used to characterize thermodynamic and gravitational equilibrium which
determines the structure of stars and predicts their instability above a
certain mass. Contraction accompanying radiation induces either heating or
cooling, which explains the formation of stars above a minimum mass. The
characteristics of the emitted light are understood from black-body radiation
and more precisely from the Boltzmann-Lorentz kinetic equation for photons. The
luminosity is governed by the transport of heat by photons from the center to
the surface. Heat production by thermonuclear fusion is determined by
microscopic balance equations. The stability of the steady state of stars is
controlled by the interplay of thermodynamics and gravitation.Comment: latex gould_last.tex, 4 files, submitted to Am. J. Phy
Small object limit of Casimir effect and the sign of the Casimir force
We show a simple way of deriving the Casimir Polder interaction, present some
general arguments on the finiteness and sign of mutual Casimir interactions and
finally we derive a simple expression for Casimir radiation from small
accelerated objects.Comment: 13 pages, late
Does the quark-gluon plasma contain stable hadronic bubbles?
We calculate the thermodynamic potential of bubbles of hadrons embedded in
quark-gluon plasma, and of droplets of quark-gluon plasma embedded in hadron
phase. This is a generalization of our previous results to the case of non-zero
chemical potentials. As in the zero chemical potential case, we find that a
quark-gluon plasma in thermodynamic equilibrium may contain stable bubbles of
hadrons of radius fm. The calculations are performed within the
MIT Bag model, using an improved multiple reflection expansion. The results are
of relevance for neutron star phenomenology and for ultrarelativistic heavy ion
collisions.Comment: 12 pages including 8 figures. To appear in Phys. Rev.
Charles Coulston GILLISPIE, Raffaele PISANO, Lazare and Sadi Carnot: A scientific and filial relationship,
Article d'étude sur le livre Charles Coulston GILLISPIE, Raffaele PISANO, Lazare and Sadi Carnot: A scientific and filial relationship,Car-not : A scientific and filial relationship, 2 de édition (Dordrecht : Springer, 2014), XVI-490 p., illustr. n. et bl. et coul., bibliogr., in-dex, « History of mechanism and machine science », vol. 19. Ce livre, « extraordinaire » comme l'écrit Eberhard Knobloch dans sa préface, porte principalement sur un événement unique dans l'histoire, la création d'une science nouvelle. Comme chacun sait, cette création de toutes pièces de la ther-modynamique est marquée par la publication en 1824 des Réflexions sur la puis-sance motrice du feu et sur les machines propres à développer cette puissance de Sadi Carnot (1796-1832). Une bonne partie du présent ouvrage est consacrée à la genèse de ce livre fondateur. Malgré le nombre immense d'études ayant porté sur cette création de la thermodynamique, les auteurs nous présentent une étude d'une grande originalité, dont l'une des lignes directrices est le rôle joué par les idées de Lazare Carnot (1753-1823) sur la pensée de son fils. Le début de l'ouvrage, qui donc concerne l'oeuvre scientifique de Lazare Carnot
The quantum measurement process in an exactly solvable model
An exactly solvable model for a quantum measurement is discussed which is
governed by hamiltonian quantum dynamics. The -component of a
spin-1/2 is measured with an apparatus, which itself consists of magnet coupled
to a bath. The initial state of the magnet is a metastable paramagnet, while
the bath starts in a thermal, gibbsian state. Conditions are such that the act
of measurement drives the magnet in the up or down ferromagnetic state
according to the sign of of the tested spin. The quantum measurement goes
in two steps. On a timescale the off-diagonal elements of the
spin's density matrix vanish due to a unitary evolution of the tested spin and
the apparatus spins; on a larger but still short timescale this is made
definite by the bath. Then the system is in a `classical' state, having a
diagonal density matrix. The registration of that state is a quantum process
which can already be understood from classical statistical mechanics. The von
Neumann collapse and the Born rule are derived rather than postulated.Comment: 7 pages revtex, 2 figure
Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula
We derive semiclassical contributions of periodic orbits from a boundary
integral equation for three-dimensional billiard systems. We use an iterative
method that keeps track of the composition of the stability matrix and the
Maslov index as an orbit is traversed. Results are given for isolated periodic
orbits and rotationally invariant families of periodic orbits in axially
symmetric billiard systems. A practical method for determining the stability
matrix and the Maslov index is described.Comment: LaTeX, 19 page
New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation
We formulate a new Bardeen-Cooper-Schrieffer (BCS)-type theory at finite
temperature, by deriving a set of variational equations of the free energy
after the particle-number projection. With its broad applicability, this theory
can be a useful tool for investigating the pairing phase transition in finite
systems with the particle-number conservation. This theory provides effects of
the symmetry-restoring fluctuation (SRF) for the pairing phenomena in finite
fermionic systems, distinctively from those of additional quantum fluctuations.
It is shown by numerical calculations that the phase transition is compatible
with the conservation in this theory, and that the SRF shifts up the critical
temperature (). This shift of occurs due to
reduction of degrees-of-freedom in canonical ensembles, and decreases only
slowly as the particle-number increases (or as the level spacing narrows), in
contrast to the conventional BCS theory.Comment: 10 pages including 3 figures, to be published in Phys. Rev.
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