8 research outputs found
Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics
A generalization of the thermodynamic uncertainty relations is proposed. It
is done by introducing of an additional term proportional to the interior
energy into the standard thermodynamic uncertainty relation that leads to
existence of the lower limit of inverse temperature. The authors are of the
opinion that the approach proposed may lead to proof of these relations. To
this end, the statistical mechanics deformation at Planck scale. The
statistical mechanics deformation is constructed by analogy to the earlier
quantum mechanical results. As previously, the primary object is a density
matrix, but now the statistical one. The obtained deformed object is referred
to as a statistical density pro-matrix. This object is explicitly described,
and it is demonstrated that there is a complete analogy in the construction and
properties of quantum mechanics and statistical density matrices at Plank scale
(i.e. density pro-matrices). It is shown that an ordinary statistical density
matrix occurs in the low-temperature limit at temperatures much lower than the
Plank's. The associated deformation of a canonical Gibbs distribution is given
explicitly.Comment: 15 pages,no figure
Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
We study two different ways to analyze the Hawking evaporation of a
Schwarzschild-de Sitter black hole. The first one uses the standard approach of
surface gravity evaluated at the possible horizons. The second method derives
its results via the Generalized Uncertainty Principle (GUP) which offers a yet
different method to look at the problem. In the case of a Schwarzschild black
hole it is known that this methods affirms the existence of a black hole
remnant (minimal mass ) of the order of Planck mass
and a corresponding maximal temperature also of the order of
. The standard dispersion relation is, in the GUP
formulation, deformed in the vicinity of Planck length which is
the smallest value the horizon can take. We generalize the uncertainty
principle to Schwarzschild-de Sitter spacetime with the cosmological constant
and find a dual relation which, compared to
and , affirms the existence of a maximal mass
of the order , minimum
temperature . As compared to the standard
approach we find a deformed dispersion relation close to
and in addition at the maximally possible horizon approximately at
. agrees with the standard results at
(or equivalently at ).Comment: new references adde