8,514 research outputs found

### Status of the Clausius inequality in classical thermodynamics

We present an analysis of the foundations of the well known Clausius
inequality. It is shown that, strictly speaking, the inequality is not a
logical consequence of the Kelvin-Planck formulation of the second law of
thermodynamics. Some thought experiments demonstrating the violation of the
Clausius inequality are considered. Also, a reformulation of the Landauer's
principle in terms of the Clausius inequality is proposed. This version of the
inequality may be considered a consequence of the fluctuation theorem.Comment: 29 pages, 9 figure

### On the sigma function identity

We consider the known functional identity on the Weierstrass sigma function.
A complete classification of odd entire functions which satisfy the same
identity is obtained.Comment: This result turns out to be very old (see Whittaker,Watson,"A Course
of Modern Analysis", ch. 20, Exercise 38). Two proofs are essentially
differen

### On the Clausius theorem

We show that for a metastable system there exists a theoretical possibility
of a violation of the Clausius inequality without a violation of the second
law. Possibilities of experimental detection of this hypothetical violation are
pointed out

### The Clausius inequality does not follow from the second law of thermodynamics

The example of macroscopic thermodynamical system violating the Clausius
inequality is presented

### Is the Clausius inequality a consequence of the second law?

We present an analysis of the foundations of the well known Clausius
inequality. It is shown that, in general, the inequality is not a logical
consequence of the Kelvin-Planck formulation of the second law of
thermodynamics. Some thought experiments demonstrating the violation of the
Clausius inequality are considered. The possibility of experimental detection
of the violation is pointed out.Comment: 14 pages, 5 figure

### X-fluid and viscous fluid in D-dimensional anisotropic integrable cosmology

D-dimensional cosmological model describing the evolution of a perfect fluid
with negative pressure (x-fluid) and a fluid possessing both shear and bulk
viscosity in n Ricci-flat spaces is investigated. The second equations of state
are chosen in some special form of metric dependence of the shear and bulk
viscosity coefficients. The equations of motion are integrated and the
dynamical properties of the exact solutions are studied. It is shown the
possibility to resolve the cosmic coincidence problem when the x-fluid plays
role of quintessence and the viscous fluid is used as cold dark matter.Comment: 11 pages, Latex 2.0

### Toda Chains with Type Am Lie Algebra for Multidimensional Classical Cosmology with Intersecting p-Branes

We consider a D-dimensional cosmological model describing an evolution of
(n+1) Einstein factor spaces in the theory with several dilatonic scalar fields
and generalized electro-magnetic forms, admitting an interpretation in terms of
intersecting p-branes. The equations of motion of the model are reduced to the
Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system.
We consider the case, when characteristic vectors of the model, related to
p-branes configuration and their couplings to the dilatonic fields, may be
interpreted as the root vectors of a Lie algebra of the type Am. The model is
reduced to the open Toda chain and integrated. The exact solution is presented
in the Kasner-like form.Comment: 13 pages, Late

### Multidimensional Cosmology with Multicomponent Perfect Fluid and Toda Lattices

The integration procedure for multidimensional cosmological models with
multicomponent perfect fluid in spaces of constant curvature is developed.
Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done.
Some known solutions are singled out from those obtained. The existence of the
wormholes is proved.Comment: 21 page

### Exact Solutions in Multidimensional Cosmology with Shear and Bulk Viscosity

Multidimensional cosmological model describing the evolution of a fluid with
shear and bulk viscosity in $n$ Ricci-flat spaces is investigated. The
barotropic equation of state for the density and the pressure in each space is
assumed. The second equation of state is chosen in the form when the bulk and
the shear viscosity coefficients are inversely proportional to the volume of
the Universe. The integrability of Einstein equations reads as a colinearity
constraint between vectors which are related to constant parameters in the
first and second equations of state. We give exact solutions in a Kasner-like
form. The processes of dynamical compactification and the entropy production
are discussed. The non-singular $D$-dimensional isotropic viscous solution is
singled out.Comment: 18 pages, Latex 2.0

### General solutions for flat Friedmann universe filled by perfect fluid and scalar field with exponential potential

We study integrability by quadrature of a spatially flat Friedmann model
containing both a minimally coupled scalar field $\phi$ with an exponential
potential $V(\phi)\sim\exp[-\sqrt{6}\sigma\kappa\phi]$, $\kappa=\sqrt{8\pi
G_N}$, of arbitrary sign and a perfect fluid with barotropic equation of state
$p=(1-h)\rho$. From the mathematical view point the model is pseudo-Euclidean
Toda-like system with 2 degrees of freedom. We apply the methods developed in
our previous papers, based on the Minkowsky-like geometry for 2 characteristic
vectors depending on the parameters $\sigma$ and $h$. In general case the
problem is reduced to integrability of a second order ordinary differential
equation known as the generalized Emden-Fowler equation, which was investigated
by discrete-group methods. We present 4 classes of general solutions for the
parameters obeying the following relations: {\bf A}. $\sigma$ is arbitrary,
$h=0$; {\bf B}. $\sigma=1-h/2$, $0<h<2$; {\bf C1}. $\sigma=1-h/4$, $0<h\leq 2$;
{\bf C2}. $\sigma=|1-h|$, $0<h\leq 2$, $h\neq 1,4/3$. We discuss the properties
of the exact solutions near the initial singularity and at the final stage of
evolution.Comment: 13 pages, Latex, 1 figure, submit. to Class. Quantum Gra

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