2,461 research outputs found
Macroscopic proof of the Jarzynski-Wojcik fluctuation theorem for heat exchange
In a recent work, Jarzynski and Wojcik (2004 Phys. Rev. Lett. 92, 230602)
have shown by using the properties of Hamiltonian dynamics and a statistical
mechanical consideration that, through contact, heat exchange between two
systems initially prepared at different temperatures obeys a fluctuation
theorem. Here, another proof is presented, in which only macroscopic
thermodynamic quantities are employed. The detailed balance condition is found
to play an essential role. As a result, the theorem is found to hold under very
general conditions.Comment: 9 pages, 0 figure
Tolman mass, generalized surface gravity, and entropy bounds
In any static spacetime the quasi-local Tolman mass contained within a volume
can be reduced to a Gauss-like surface integral involving the flux of a
suitably defined generalized surface gravity. By introducing some basic
thermodynamics and invoking the Unruh effect one can then develop elementary
bounds on the quasi-local entropy that are very similar in spirit to the
holographic bound, and closely related to entanglement entropy.Comment: V1: 4 pages. Uses revtex4-1; V2: Three references added; V3: Some
notational changes for clarity; introductory paragraph rewritten; no physics
changes. This version accepted for publication in Physical Review Letter
Planck Fluctuations, Measurement Uncertainties and the Holographic Principle
Starting from a critical analysis of recently reported surprisingly large
uncertainties in length and position measurements deduced within the framework
of quantum gravity, we embark on an investigation both of the correlation
structure of Planck scale fluctuations and the role the holographic hypothesis
is possibly playing in this context. While we prove the logical independence of
the fluctuation results and the holographic hypothesis (in contrast to some
recent statements in that direction) we show that by combining these two topics
one can draw quite strong and interesting conclusions about the fluctuation
structure and the microscopic dynamics on the Planck scale. We further argue
that these findings point to a possibly new and generalized form of quantum
statistical mechanics of strongly (anti)correlated systems of degrees of
freedom in this fundamental regime.Comment: 19 pages, Latex, no figures, some new references, to appear
ModPhysLett
Gravitational energy
Observers at rest in a stationary spacetime flat at infinity can measure
small amounts of rest-mass+internal energies+kinetic energies+pressure energy
in a small volume of fluid attached to a local inertial frame. The sum of these
small amounts is the total "matter energy" for those observers. The total
mass-energy minus the matter energy is the binding gravitational energy.
Misner, Thorne and Wheeler evaluated the gravitational energy of a
spherically symmetric static spacetime. Here we show how to calculate
gravitational energy in any static and stationary spacetime for isolated
sources with a set of observers at rest.
The result of MTW is recovered and we find that electromagnetic and
gravitational 3-covariant energy densities in conformastatic spacetimes are of
opposite signs. Various examples suggest that gravitational energy is negative
in spacetimes with special symmetries or when the energy-momentum tensor
satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra
Fluctuation theorem for the renormalized entropy change in the strongly nonlinear nonequilibrium regime
Generalizing a recent work [T. Taniguchi and E. G. D. Cohen, J. Stat. Phys.
126, 1 (2006)] that was based on the Onsager-Machlup theory, a nonlinear
relaxation process is considered for a macroscopic thermodynamic quantity. It
is found that the fluctuation theorem holds in the nonlinear nonequilibrium
regime if the change of the entropy characterized by local equilibria is
appropriately renormalized. The fluctuation theorem for the ordinary entropy
change is recovered in the linear near-equilibrium case. This result suggests a
possibility that the the information-theoretic entropy of the Shannon form may
be modified in the strongly nonlinear nonequilibrium regime.Comment: 14 pages, no figures. Typos correcte
On the stable configuration of ultra-relativistic material spheres. The solution for the extremely hot gas
During the last stage of collapse of a compact object into the horizon of
events, the potential energy of its surface layer decreases to a negative value
below all limits. The energy-conservation law requires an appearance of a
positive-valued energy to balance the decrease. We derive the internal-state
properties of the ideal gas situated in an extremely strong, ultra-relativistic
gravitational field and suggest to apply our result to a compact object with
the radius which is slightly larger than or equal to the Schwarzschild's
gravitational radius. On the surface of the object, we find that the extreme
attractivity of the gravity is accompanied with an extremely high internal,
heat energy. This internal energy implies a correspondingly high pressure, the
gradient of which has such a behavior that it can compete with the gravity. In
a more detail, we find the equation of state in the case when the magnitude of
the potential-type energy of constituting gas particles is much larger than
their rest energy. This equation appears to be identical with the
general-relativity condition of the equilibrium between the gravity and
pressure gradient. The consequences of the identity are discussed.Comment: 12 pages (no figure, no table) Changes in 3-rd version: added an
estimate of neutrino cooling and relative time-scale of the final stage of
URMS collaps
Papapetrou Energy-Momentum Tensor for Chern-Simons Modified Gravity
We construct a conserved, symmetric energy-momentum (pseudo-)tensor for
Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz
invariant. The tensor is discussed in relation to other gravitational
energy-momentum tensors and analyzed for the Schwarzschild, Reissner-Nordstrom,
and FRW solutions. To our knowledge this is the first confirmation that the
Reissner-Nordstrom and FRW metrics are solutions of the modified theory.Comment: 8 pages; typos corrected, references fixed, some calculations
shortene
Statistical mechanical theory of an oscillating isolated system. The relaxation to equilibrium
In this contribution we show that a suitably defined nonequilibrium entropy
of an N-body isolated system is not a constant of the motion in general and its
variation is bounded, the bounds determined by the thermodynamic entropy, i.e.,
the equilibrium entropy. We define the nonequilibrium entropy as a convex
functional of the set of n-particle reduced distribution functions
(n=0,......., N) generalizing the Gibbs fine-grained entropy formula.
Additionally, as a consequence of our microscopic analysis we find that this
nonequilibrium entropy behaves as a free entropic oscillator. In the approach
to the equilibrium regime we find relaxation equations of the Fokker-Planck
type, particularly for the one-particle distribution function
Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame
The Planck spectrum of thermal scalar radiation is derived suggestively
within classical physics by the use of an accelerating coordinate frame. The
derivation has an analogue in Boltzmann's derivation of the Maxwell velocity
distribution for thermal particle velocities by considering the thermal
equilibrium of noninteracting particles in a uniform gravitational field. For
the case of radiation, the gravitational field is provided by the acceleration
of a Rindler frame through Minkowski spacetime. Classical zero-point radiation
and relativistic physics enter in an essential way in the derivation which is
based upon the behavior of free radiation fields and the assumption that the
field correlation functions contain but a single correlation time in thermal
equilibrium. The work has connections with the thermal effects of acceleration
found in relativistic quantum field theory.Comment: 23 page
Integral Constraints On cosmological Perturbations and their Energy
We show the relation between Traschen's integral equations and the energy,
and ``position of the centre of mass'', of the matter perturbations in a
Robertson-Walker spacetime. When the perturbations are ``localised'' we get a
set of integral constraints that includes hers. We illustrate them on a simple
example.Comment: 19 pages, Tex file, submitted to Classical and Quantum Gravit
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