6,162 research outputs found
Universal restrictions to the conversion of heat into work derived from the analysis of the Nernst theorem as a uniform limit
We revisit the relationship between the Nernst theorem and the Kelvin-Planck
statement of the second law. We propose that the exchange of entropy uniformly
vanishes as the temperature goes to zero. The analysis of this assumption shows
that is equivalent to the fact that the compensation of a Carnot engine scales
with the absorbed heat so that the Nernst theorem should be embedded in the
statement of the second law.
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Se analiza la relaci{\'o}n entre el teorema de Nernst y el enunciado de
Kelvin-Planck del segundo principio de la termodin{\'a}mica. Se{\~n}alamos el
hecho de que el cambio de entrop{\'\i}a tiende uniformemente a cero cuando la
temperatura tiende a cero. El an{\'a}lisis de esta hip{\'o}tesis muestra que es
equivalente al hecho de que la compensaci{\'o}n de una m{\'a}quina de Carnot
escala con el calor absorbido del foco caliente, de forma que el teorema de
Nernst puede derivarse del enunciado del segundo principio.Comment: 8pp, 4 ff. Original in english. Also available translation into
spanish. Twocolumn format. RevTe
Four lectures on secant varieties
This paper is based on the first author's lectures at the 2012 University of
Regina Workshop "Connections Between Algebra and Geometry". Its aim is to
provide an introduction to the theory of higher secant varieties and their
applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in
Mathematics & Statistics), Springer/Birkhause
Thermodynamic fluctuation relation for temperature and energy
The present work extends the well-known thermodynamic relation for the canonical ensemble. We start from the general
situation of the thermodynamic equilibrium between a large but finite system of
interest and a generalized thermostat, which we define in the course of the
paper. The resulting identity can account for thermodynamic states
with a negative heat capacity ; at the same time, it represents a
thermodynamic fluctuation relation that imposes some restrictions on the
determination of the microcanonical caloric curve . Finally, we comment briefly on the implications of the present
result for the development of new Monte Carlo methods and an apparent analogy
with quantum mechanics.Comment: Version accepted for publication in J. Phys. A: Math and The
Is it still worth searching for lepton flavor violation in rare kaon decays?
Prospective searches for lepton flavor violation (LFV) in rare kaon decays at
the existing and future intermediate-energy accelerators are considered. The
proposed studies are complementary to LFV searches in muon-decay experiments
and offer a unique opportunity to probe models with approximately conserved
fermion-generation quantum number with sensitivity superior to that in other
processes. Consequently, new searches for LFV in kaon decays are an important
and independent part of the general program of searches for lepton flavor
violation in the final states with charged leptons.Comment: 30 pages, 10 figures. An extended version of the talk given at the
Chicago Flavor Seminar, February 27, 2004. In the new version some misprints
were corrected and some new data for LFV-processes were added. The main
content of the paper was not changed. The paper is published in Yad. Fiz. 68,
1272 (2005
Decomposition of homogeneous polynomials with low rank
Let be a homogeneous polynomial of degree in variables defined
over an algebraically closed field of characteristic zero and suppose that
belongs to the -th secant varieties of the standard Veronese variety
but that its minimal
decomposition as a sum of -th powers of linear forms is
with . We show that if then such a
decomposition of can be split in two parts: one of them is made by linear
forms that can be written using only two variables, the other part is uniquely
determined once one has fixed the first part. We also obtain a uniqueness
theorem for the minimal decomposition of if the rank is at most and a
mild condition is satisfied.Comment: final version. Math. Z. (to appear
Notes on the Third Law of Thermodynamics.I
We analyze some aspects of the third law of thermodynamics. We first review
both the entropic version (N) and the unattainability version (U) and the
relation occurring between them. Then, we heuristically interpret (N) as a
continuity boundary condition for thermodynamics at the boundary T=0 of the
thermodynamic domain. On a rigorous mathematical footing, we discuss the third
law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's
approach is fundamental in order to understand the nature of the surface T=0.
In fact, in this approach, under suitable mathematical conditions, T=0 appears
as a leaf of the foliation of the thermodynamic manifold associated with the
non-singular integrable Pfaffian form . Being a leaf, it cannot
intersect any other leaf const. of the foliation. We show that (N) is
equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the
peculiar nature of T=0 appears to be less evident because the existence of the
entropy is a postulate; nevertheless, it is still possible to conclude that the
lowest value of the entropy has to belong to the boundary of the convex set
where the function is defined.Comment: 29 pages, 2 figures; RevTex fil
Photoproduction evidence for and against hidden-strangeness states near 2 GeV
Experimental evidence from coherent diffractive proton scattering has been
reported for two narrow baryonic resonances which decay predominantly to
strange particles. These states, with masses close to 2.0 GeV would, if
confirmed, be candidates for hidden strangeness states with unusual internal
structure. In this paper we examine the literature on strangeness
photoproduction, to seek additional evidence for or against these states. We
find that one state is not confirmed, while for the other state there is some
mild supporting evidence favoring its existence. New experiments are called
for, and the expected photoproduction lineshapes are calculated.Comment: 9 pages, RevTex, five postscript figures, submitted to PR
Chemical Potential and the Nature of the Dark Energy: The case of phantom
The influence of a possible non zero chemical potential on the nature
of dark energy is investigated by assuming that the dark energy is a
relativistic perfect simple fluid obeying the equation of state (EoS),
(). The entropy condition, ,
implies that the possible values of are heavily dependent on the
magnitude, as well as on the sign of the chemical potential. For , the
-parameter must be greater than -1 (vacuum is forbidden) while for not only the vacuum but even a phantomlike behavior () is
allowed. In any case, the ratio between the chemical potential and temperature
remains constant, that is, . Assuming that the dark energy
constituents have either a bosonic or fermionic nature, the general form of the
spectrum is also proposed. For bosons is always negative and the extended
Wien's law allows only a dark component with which includes
vacuum and the phantomlike cases. The same happens in the fermionic branch for
are permmited only if . The thermodynamics and statistical arguments constrain the
EoS parameter to be , a result surprisingly close to the maximal
value required to accelerate a FRW type universe dominated by matter and dark
energy ().Comment: 7 pages, 5 figure
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