15,632 research outputs found
Inverse Temperature 4-vector in Special Relativity
There exist several prescriptions for identifying the notion of temperature
in special relativity. We argue that the inverse temperature 4-vector is the only viable option from the laws of thermodynamics, and is a future-directed timelike 4-vector. Using a superfluidity thought
experiment, one can show that is not necessarily along the time
direction of the comoving frame of the system, as is usually thought. It is
conjectured that, for an isolated system, the 4-vector is determined from the
entropy-maximum principle.Comment: 11 pages, revised versio
Covariant statistical mechanics and the stress-energy tensor
After recapitulating the covariant formalism of equilibrium statistical
mechanics in special relativity and extending it to the case of a non-vanishing
spin tensor, we show that the relativistic stress-energy tensor at
thermodynamical equilibrium can be obtained from a functional derivative of the
partition function with respect to the inverse temperature four-vector \beta.
For usual thermodynamical equilibrium, the stress-energy tensor turns out to be
the derivative of the relativistic thermodynamic potential current with respect
to the four-vector \beta, i.e. T^{\mu \nu} = - \partial \Phi^\mu/\partial
\beta_\nu. This formula establishes a relation between stress-energy tensor and
entropy current at equilibrium possibly extendable to non-equilibrium
hydrodynamics.Comment: 4 pages. Final version accepted for publication in Phys. Rev. Let
Thermodynamics of Extended Bodies in Special Relativity
Relativistic thermodynamics is generalized to accommodate four dimensional
rotation in a flat spacetime. An extended body can be in equilibrium when its
each element moves along a Killing flow. There are three types of basic Killing
flows in a flat spacetime, each of which corresponds to translational motion,
spatial rotation, and constant linear acceleration; spatial rotation and
constant linear acceleration are regarded as four dimensional rotation.
Translational motion has been mainly investigated in the past literature of
relativistic thermodynamics. Thermodynamics of the other two is derived in the
present paper.Comment: 8 pages, no figur
Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity
Between Snyder's quantized space-time model in de Sitter space of momenta and
the \dS special relativity on \dS-spacetime of radius with Beltrami
coordinates, there is a one-to-one dual correspondence supported by a minimum
uncertainty-like argument. Together with Planck length , should be a fundamental constant. They lead to a
dimensionless constant . These indicate that physics at these two scales should be dual to
each other and there is in-between gravity of local \dS-invariance
characterized by . A simple model of \dS-gravity with a gauge-like action on
umbilical manifolds may show these characters. It can pass the observation
tests and support the duality.Comment: 32 page
Nonlocal observables and lightcone-averaging in relativistic thermodynamics
The unification of relativity and thermodynamics has been a subject of
considerable debate over the last 100 years. The reasons for this are twofold:
(i) Thermodynamic variables are nonlocal quantities and, thus, single out a
preferred class of hyperplanes in spacetime. (ii) There exist different,
seemingly equally plausible ways of defining heat and work in relativistic
systems. These ambiguities led, for example, to various proposals for the
Lorentz transformation law of temperature. Traditional 'isochronous'
formulations of relativistic thermodynamics are neither theoretically
satisfactory nor experimentally feasible. Here, we demonstrate how these
deficiencies can be resolved by defining thermodynamic quantities with respect
to the backward-lightcone of an observation event. This approach yields novel,
testable predictions and allows for a straightforward-extension of
thermodynamics to General Relativity. Our theoretical considerations are
illustrated through three-dimensional relativistic many-body simulations.Comment: typos in Eqs. (12) and (14) corrected, minor additions in the tex
On the interaction between two Kerr black holes
The double-Kerr solution is generated using both a Backlund transformation
and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary
between the parametrisations naturally obtained in the two methods and show
their equivalence. We then focus on the asymptotically flat double-Kerr system
obeying the axis condition which is Z_2^\phi invariant; for this system there
is an exact formula for the force between the two black holes, in terms of
their physical quantities and the coordinate distance. We then show that 1) the
angular velocity of the two black holes decreases from the usual Kerr value at
infinite distance to zero in the touching limit; 2) the extremal limit of the
two black holes is given by |J|=cM^2, where c depends on the distance and
varies from one to infinity as the distance decreases; 3) for sufficiently
large angular momentum the temperature of the black holes attains a maximum at
a certain finite coordinate distance. All of these results are interpreted in
terms of the dragging effects of the system.Comment: 19 pages, 4 figures. v2: changed statement about thermodynamical
equilibrium in section 3; minor changes; added references. v3: added
references to previous relevant work; removed one equation (see note added);
other minor corrections; final version to be published in JHE
Statistical mechanics in the context of special relativity II
The special relativity laws emerge as one-parameter (light speed)
generalizations of the corresponding laws of classical physics. These
generalizations, imposed by the Lorentz transformations, affect both the
definition of the various physical observables (e.g. momentum, energy, etc), as
well as the mathematical apparatus of the theory. Here, following the general
lines of [Phys. Rev. E {\bf 66}, 056125 (2002)], we show that the Lorentz
transformations impose also a proper one-parameter generalization of the
classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy
permits to construct a coherent and selfconsistent relativistic statistical
theory, preserving the main features of the ordinary statistical theory, which
recovers in the classical limit. The predicted distribution function is a
one-parameter continuous deformation of the classical Maxwell-Boltzmann
distribution and has a simple analytic form, showing power law tails in
accordance with the experimental evidence. Furthermore the new statistical
mechanics can be obtained as stationary case of a generalized kinetic theory
governed by an evolution equation obeying the H-theorem and reproducing the
Boltzmann equation of the ordinary kinetics in the classical limit.Comment: 14 pages, no figures, proof correction
Cosmological Production of Vector Bosons and Cosmic Microwave Background Radiation
The intensive cosmological creation of vector W, Z- bosons in the
cosmological model with the relative units is considered. Field theoretical
models are studied, which predict that the CMB radiation and the baryon matter
in the universe can be products of decay and annihilation processes of these
primordial bosons.Comment: 31 pages, 1 figur
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