213 research outputs found
The Concept of Temperature in the Modern Physics
The physical quantity "temperature" is a cornerstone of thermodynamics and
statistical physics. But it is necessary to mention that very frequently the
scientists forget about the conditions to be satisfied in order to introduce
"temperature" in macroscopic physics. In the present paper the short
introduction to the classical concept of temperature for macroscopic
equilibrium systems will be given. The concept of "spin temperature" in
condensed matter physics will be reviewed and the advantages of thermodynamic
approach to the problems of magnetism will be illustrated. Finally, the concept
of temperature will be discussed regarding the nanoscale physics and
non-extensive systems.Comment: 4 figures, InTech class file included, accepted for publication in
"Thermodynamics - Systems in Equilibrium and Non-Equilibrium" ISBN
979-953-307-047-5, edited by J. C. M. Piraj\'a
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis
The novelty of the Jean Pierre Badiali last scientific works stems to a
quantum approach based on both (i) a return to the notion of trajectories
(Feynman paths) and (ii) an irreversibility of the quantum transitions. These
iconoclastic choices find again the Hilbertian and the von Neumann algebraic
point of view by dealing statistics over loops. This approach confers an
external thermodynamic origin to the notion of a quantum unit of time (Rovelli
Connes' thermal time). This notion, basis for quantization, appears herein as a
mere criterion of parting between the quantum regime and the thermodynamic
regime. The purpose of this note is to unfold the content of the last five
years of scientific exchanges aiming to link in a coherent scheme the Jean
Pierre's choices and works, and the works of the authors of this note based on
hyperbolic geodesics and the associated role of Riemann zeta functions. While
these options do not unveil any contradictions, nevertheless they give birth to
an intrinsic arrow of time different from the thermal time. The question of the
physical meaning of Riemann hypothesis as the basis of quantum mechanics, which
was at the heart of our last exchanges, is the backbone of this note.Comment: 13 pages, 2 figure
Fractal geometry, information growth and nonextensive thermodynamics
This is a study of the information evolution of complex systems by
geometrical consideration. We look at chaotic systems evolving in fractal phase
space. The entropy change in time due to the fractal geometry is assimilated to
the information growth through the scale refinement. Due to the incompleteness
of the state number counting at any scale on fractal support, the incomplete
normalization is applied throughout the paper, where is the
fractal dimension divided by the dimension of the smooth Euclidean space in
which the fractal structure of the phase space is embedded. It is shown that
the information growth is nonadditive and is proportional to the trace-form
which can be connected to several nonadditive
entropies. This information growth can be extremized to give power law
distributions for these non-equilibrium systems. It can also be used for the
study of the thermodynamics derived from Tsallis entropy for nonadditive
systems which contain subsystems each having its own . It is argued that,
within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can
be preserved.Comment: Final version, 10 pages, no figures, Invited talk at the
international conference NEXT2003, 21-28 september 2003, Villasimius
(Cagliari), Ital
A mathematical structure for the generalization of the conventional algebra
An abstract mathematical framework is presented in this paper as a
unification of several deformed or generalized algebra proposed recently in the
context of generalized statistical theories intended to treat certain complex
thermodynamic or statistical systems. It is shown that, from mathematical point
of view, any bijective function can be used in principle to formulate an
algebra in which the conventional algebraic rules are generalized
Stable local bases for multivariate spline spaces
We present an algorithm for constructing stable local bases for the spaces Srd(Δ) of multivariate polynomial splines of smoothness r⩾1 and degree d⩾r2n+1 on an arbitrary triangulation Δ of a bounded polyhedral domain Ω⊂n, n⩾2
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