11 research outputs found
Three tests of general relativity via Fermat's principle and the phase of Bessel functions
Fermat's principle applied to a flat metric in the plane yields the phase of
a Bessel function in the periodic domain for a constant index of refraction.
Gravitational forces cause the index of refraction to vary and lead to a
modified phase of the Bessel function. A distinction is made between the forces
that cause acceleration: the gravitational force affects the optical properties
of the medium whereas the centrifugal force does not, the latter being built
into the phase of oscillations of the Bessel function. The time delay in radar
echoes from planets is determined from Fermat's principle where the velocity of
light is the phase velocity and the index of refraction varies on account of
the gravitational potential. The deflection of light by a massive body is shown
to be produced by a quadrupole interaction, and the perihelion shift requires
both the gravitational potential, producing a closed orbit, and the quadrupole,
causing the perihelion to rotate.Comment: 16 page
Gibbs' Paradox according to Gibbs and slightly beyond
The so-called Gibbs paradox is a paradigmatic narrative illustrating the necessity to account for
the N! ways of permuting N identical particles when summing over microstates. Yet, there exist
some mixing scenarios for which the expected thermodynamic outcome depends on the viewpoint
one chooses to justify this combinatorial term. After a brief summary on Gibbs' paradox and what is
the standard rationale used to justify its resolution, we will allow ourself to question from a historical
standpoint whether the Gibbs paradox has actually anything to do with Gibbs' work. In so doing,
we also aim at shedding a new light with regards to some of the theoretical claims surrounding its
resolution. We will then turn to the statistical thermodynamics of discrete and continuous mixtures
and introduce the notion of composition entropy to characterise these systems. This will enable us to
address, in a certain sense, a "curiosity" pointed out by Gibbs in a paper published in 1876. Finally,
we will �nish by proposing a connexion between the results we propose and a recent extension of
the Landauer bound regarding the minimum amount of heat to be dissipated to reset one bit of
memory
Consequences of temperature fluctuations in observables measured in high energy collisions
We review the consequences of intrinsic, nonstatistical temperature
fluctuations as seen in observables measured in high energy collisions. We do
this from the point of view of nonextensive statistics and Tsallis
distributions. Particular attention is paid to multiplicity fluctuations as a
first consequence of temperature fluctuations, to the equivalence of
temperature and volume fluctuations, to the generalized thermodynamic
fluctuations relations allowing us to compare fluctuations observed in
different parts of phase space, and to the problem of the relation between
Tsallis entropy and Tsallis distributions. We also discuss the possible
influence of conservation laws on these distributions and provide some examples
of how one can get them without considering temperature fluctuations.Comment: Revised version of the invited contribution to The European Physical
Journal A (Hadrons and Nuclei) topical issue about 'Relativistic Hydro- and
Thermodynamics in Nuclear Physics' guest eds. Tamas S. Biro, Gergely G.
Barnafoldi and Peter Va
Relativistic Thermodynamics and the Classical Model of the Electron
Einstein's famous relation between mass and energy is interpreted in terms of the equivalence of the rate of heating of a body and the rate of increase of its inertial mass. In an adiabatic process, where the proper mass remains constant, it is the heat content, and not the energy, which is conserved because the pressure, and not the volume, is Lorentz-invariant. There are two categories of relativistic quantities: inertial and thermodynamic ones, which are transformed into one another by the work necessary to keep the inertial state in motion. In a non-adiabatic process, the rate of heating is Lorentz-invariant, which must always be greater than the power that it generates
Concerning Tsallis`s Condition of Pseudo-additivity as a Definition of Non-extensivity and the Use of the Maximum Entropy Formalism
Adult education, community development and rural regeneration Synopsis report of the Rural Development and Regeneration Project
An Interreg Project funded by the European UnionAvailable from British Library Document Supply Centre- DSC:q95/16766 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo