7,684 research outputs found
A Fresh Look at Entropy and the Second Law of Thermodynamics
This paper is a non-technical, informal presentation of our theory of the
second law of thermodynamics as a law that is independent of statistical
mechanics and that is derivable solely from certain simple assumptions about
adiabatic processes for macroscopic systems. It is not necessary to assume
a-priori concepts such as "heat", "hot and cold", "temperature". These are
derivable from entropy, whose existence we derive from the basic assumptions.
See cond-mat/9708200 and math-ph/9805005.Comment: LaTex file. To appear in the April 2000 issue of PHYSICS TODA
Black Holes at the LHC
If the scale of quantum gravity is near a TeV, the LHC will be producing one
black hole (BH) about every second. The BH decays into prompt, hard photons and
charged leptons is a clean signature with low background. The absence of
significant missing energy allows the reconstruction of the mass of the
decaying BH. The correlation between the BH mass and its temperature, deduced
from the energy spectrum of the decay products, can test experimentally the
higher dimensional Hawking evaporation law. It can also determine the number of
large new dimensions and the scale of quantum gravity.Comment: 5 pages, 3 figures, submitted to PRL. Results presented at the Les
Houches Workshop "Physics at the TeV Colliders" (May 30, 2001) and the
"Avatars of M-Theory" conference, ITP at Santa Barbara (June 7, 2001),
http://online.itp.ucsb.edu/online/mtheory_c01/dimopoulo
Discovering New Physics in the Decays of Black Holes
If the scale of quantum gravity is near a TeV, the LHC will be producing one
black hole (BH) about every second, thus qualifying as a BH factory. With the
Hawking temperature of a few hundred GeV, these rapidly evaporating BHs may
produce new, undiscovered particles with masses ~100 GeV. The probability of
producing a heavy particle in the decay depends on its mass only weakly, in
contrast with the exponentially suppressed direct production. Furthemore, BH
decays with at least one prompt charged lepton or photon correspond to the
final states with low background. Using the Higgs boson as an example, we show
that it may be found at the LHC on the first day of its operation, even with
incomplete detectors.Comment: 4 pages, 3 figure
Quasi-Homogeneous Thermodynamics and Black Holes
We propose a generalized thermodynamics in which quasi-homogeneity of the
thermodynamic potentials plays a fundamental role. This thermodynamic formalism
arises from a generalization of the approach presented in paper [1], and it is
based on the requirement that quasi-homogeneity is a non-trivial symmetry for
the Pfaffian form . It is shown that quasi-homogeneous
thermodynamics fits the thermodynamic features of at least some
self-gravitating systems. We analyze how quasi-homogeneous thermodynamics is
suggested by black hole thermodynamics. Then, some existing results involving
self-gravitating systems are also shortly discussed in the light of this
thermodynamic framework. The consequences of the lack of extensivity are also
recalled. We show that generalized Gibbs-Duhem equations arise as a consequence
of quasi-homogeneity of the thermodynamic potentials. An heuristic link between
this generalized thermodynamic formalism and the thermodynamic limit is also
discussed.Comment: 39 pages, uses RevteX. Published version (minor changes w.r.t. the
original one
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
Black Holes at Future Colliders and Beyond: a Topical Review
One of the most dramatic consequences of low-scale (~1 TeV) quantum gravity
in models with large or warped extra dimension(s) is copious production of mini
black holes at future colliders and in ultra-high-energy cosmic ray collisions.
Hawking radiation of these black holes is expected to be constrained mainly to
our three-dimensional world and results in rich phenomenology. In this topical
review we discuss the current status of astrophysical observations of black
holes and selected aspects of mini black hole phenomenology, such as production
at colliders and in cosmic rays, black hole decay properties, Hawking radiation
as a sensitive probe of the dimensionality of extra space, as well as an
exciting possibility of finding new physics in the decays of black holes.Comment: 31 pages, 10 figures To appear in the Journal of Physics
Accessibility of physical states and non-uniqueness of entanglement measure
Ordering physical states is the key to quantifying some physical property of
the states uniquely. Bipartite pure entangled states are totally ordered under
local operations and classical communication (LOCC) in the asymptotic limit and
uniquely quantified by the well-known entropy of entanglement. However, we show
that mixed entangled states are partially ordered under LOCC even in the
asymptotic limit. Therefore, non-uniqueness of entanglement measure is
understood on the basis of an operational notion of asymptotic convertibility.Comment: 8 pages, 1 figure. v2: main result unchanged but presentation
extensively changed. v3: figure added, minor correction
Performance of discrete heat engines and heat pumps in finite time
The performance in finite time of a discrete heat engine with internal
friction is analyzed. The working fluid of the engine is composed of an
ensemble of noninteracting two level systems. External work is applied by
changing the external field and thus the internal energy levels. The friction
induces a minimal cycle time. The power output of the engine is optimized with
respect to time allocation between the contact time with the hot and cold baths
as well as the adiabats. The engine's performance is also optimized with
respect to the external fields. By reversing the cycle of operation a heat pump
is constructed. The performance of the engine as a heat pump is also optimized.
By varying the time allocation between the adiabats and the contact time with
the reservoir a universal behavior can be identified. The optimal performance
of the engine when the cold bath is approaching absolute zero is studied. It is
found that the optimal cooling rate converges linearly to zero when the
temperature approaches absolute zero.Comment: 45 pages LaTeX, 25 eps figure
Role of five-quark components in radiative and strong decays of the Lambda(1405) resonance
Within an extended chiral constituent quark model, three- and five-quark
structure of the resonance is investigated. Helicity
amplitudes for the electromagnetic decays (, ), and transition amplitudes for
strong decays (, ) are drived, as
well as the relevant decay widths. The experimental value for the strong decay
width, MeV, is well
reproduced with about 50% of five-quark admixture in the .
Important effects due to the configuration mixings among
, and are
found. In addition, transitions between the three- and five-quark components in
the baryons turn out to be significant in both radiative and strong decays of
the resonance.Comment: typos and numerical mistakes corrected, to appear in Phys. Rev.
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
- …