2,203 research outputs found
How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems
The maximum entropy principle (MEP) is a method for obtaining the most likely
distribution functions of observables from statistical systems, by maximizing
entropy under constraints. The MEP has found hundreds of applications in
ergodic and Markovian systems in statistical mechanics, information theory, and
statistics. For several decades there exists an ongoing controversy whether the
notion of the maximum entropy principle can be extended in a meaningful way to
non-extensive, non-ergodic, and complex statistical systems and processes. In
this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related
to multiplicities of independent random processes. We then show how the
relaxation of independence naturally leads to the most general entropies that
are compatible with the first three Shannon-Khinchin axioms, the
(c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept
for non-ergodic and complex statistical systems if their relative entropy can
be factored into a generalized multiplicity and a constraint term. The problem
of finding such a factorization reduces to finding an appropriate
representation of relative entropy in a linear basis. In a particular example
we show that path-dependent random processes with memory naturally require
specific generalized entropies. The example is the first exact derivation of a
generalized entropy from the microscopic properties of a path-dependent random
process.Comment: 6 pages, 1 figure. To appear in PNA
Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
Decoherent histories quantum theory is reformulated with the assumption that
there is one "real" fine-grained history, specified in a preferred complete set
of sum-over-histories variables. This real history is described by embedding it
in an ensemble of comparable imagined fine-grained histories, not unlike the
familiar ensemble of statistical mechanics. These histories are assigned
extended probabilities, which can sometimes be negative or greater than one. As
we will show, this construction implies that the real history is not completely
accessible to experimental or other observational discovery. However,
sufficiently and appropriately coarse-grained sets of alternative histories
have standard probabilities providing information about the real fine-grained
history that can be compared with observation. We recover the probabilities of
decoherent histories quantum mechanics for sets of histories that are recorded
and therefore decohere. Quantum mechanics can be viewed as a classical
stochastic theory of histories with extended probabilities and a well-defined
notion of reality common to all decoherent sets of alternative coarse-grained
histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment
Neutrino Models of Dark Energy
I consider a scenario proposed by Fardon, Nelson and Weiner where dark energy
and neutrinos are connected. As a result, neutrino masses are not constant but
depend on the neutrino number density. By examining the full equation of state
for the dark sector, I show that in this scenario the dark energy is equivalent
to having a cosmological constant, but one that "runs" as the neutrino mass
changes with temperature. Two examples are examined that illustrate the
principal feautures of the dark sector of this scenario. In particular, the
cosmological constant is seen to be negligible for most of the evolution of the
Universe, becoming inportant only when neutrinos become non-relativistic. Some
speculations on features of this scenario which might be present in a more
realistic theory are also presented.Comment: 12 pages, 6 figures. Added comments on why FNW scenario always leads
to a running cosmological constant and a few references. To be published in
Phys. Rev.
Possible evidence of extended objects inside the proton
Recent experimental determinations of the Nachtmann moments of the inelastic
structure function of the proton F2p(x, Q**2), obtained at Jefferson Lab, are
analyzed for values of the squared four-momentum transfer Q**2 ranging from ~
0.1 to ~ 2 (GeV/c)**2. It is shown that such inelastic proton data exhibit a
new type of scaling behavior and that the resulting scaling function can be
interpreted as a constituent form factor consistent with the elastic nucleon
data. These findings suggest that at low momentum transfer the inclusive proton
structure function originates mainly from the elastic coupling with extended
objects inside the proton. We obtain a constituent size of ~ 0.2 - 0.3 fm.Comment: 1 reference adde
Decoherence Functional and Probability Interpretation
We confirm that the diagonal elements of the Gell-Mann and Hartle's
decoherence decoherence functional are equal to the relative frequencies of the
results of many identical experiments, when a set of alternative histories
decoheres. We consider both cases of the pure and mixed initial states.Comment: 9 pages, UCSBTH-92-40 and MMC-M-
Generalized entropies and the transformation group of superstatistics
Superstatistics describes statistical systems that behave like superpositions
of different inverse temperatures , so that the probability distribution
is , where the `kernel' is nonnegative and normalized
(). We discuss the relation between this distribution
and the generalized entropic form . The first three
Shannon-Khinchin axioms are assumed to hold. It then turns out that for a given
distribution there are two different ways to construct the entropy. One
approach uses escort probabilities and the other does not; the question of
which to use must be decided empirically. The two approaches are related by a
duality. The thermodynamic properties of the system can be quite different for
the two approaches. In that connection we present the transformation laws for
the superstatistical distributions under macroscopic state changes. The
transformation group is the Euclidean group in one dimension.Comment: 5 pages, no figur
Numerical indications of a q-generalised central limit theorem
We provide numerical indications of the -generalised central limit theorem
that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics.
We focus on binary random variables correlated in a {\it scale-invariant}
way. The correlations are introduced by imposing the Leibnitz rule on a
probability set based on the so-called -product with . We show
that, in the large limit (and after appropriate centering, rescaling, and
symmetrisation), the emerging distributions are -Gaussians, i.e., , with , and
with coefficients approaching finite values . The
particular case recovers the celebrated de Moivre-Laplace theorem.Comment: Minor improvements and corrections have been introduced in the new
version. 7 pages including 4 figure
Neutrino Mass Matrices with a Texture Zero and a Vanishing Minor
We study the implications of the simultaneous existence of a texture zero and
a vanishing minor in the neutrino mass matrix. There are thirty six possible
texture structures of this type, twenty one of which reduce to two texture zero
cases which have, already, been extensively studied. Of the remaining fifteen
textures only six are allowed by the current data. We examine the
phenomenological implications of the allowed texture structures for Majorana
type CP-violating phases, 1-3 mixing angle and Dirac type CP-violating phase.
All these possible textures can be generated through the seesaw mechanism and
realized in the framework of discrete abelian flavor symmetry. We present the
symmetry realization of these texture structures.Comment: To appear in Phys. Rev.
Neutrino Mixing Predictions of a Minimal SO(10) Model with Suppressed Proton Decay
During the past year, a minimal renormalizable supersymmetric SO(10) model
has been proposed with the following properties: it predicts a naturally stable
dark matter and neutrino mixing angles theta_atm and theta_13 while at the same
time accommodating CKM CP violation among quarks with no SUSY CP problem.
Suppression of proton decay for all allowed values of tan beta strongly
restricts the flavor structure of the model making it predictive for other
processes as well. We discuss the following predictions of the model in this
paper, e.g. down-type quark masses, and neutrino oscillation parameters, U_e3,
delta_MNSP, which will be tested by long baseline experiments such as T2K and
subsequent experiments using the neutrino beam from JPARC. We also calculate
lepton flavor violation and the lepton asymmetry of the Universe in this model.Comment: 22 pages, 11 figure
Constraints on leptogenesis from a symmetry viewpoint
It is shown that type I seesaw models based on the standard model Lagrangian
extended with three heavy Majorana right-handed fields do not have leptogenesis
in leading order, if the symmetries of mass matrices are also the residual
symmetry of the Lagrangian. In particular, flavor models that lead to a
mass-independent leptonic mixing have a vanishing leptogenesis CP asymmetry.
Based on symmetry arguments, we prove that in these models the Dirac-neutrino
Yukawa coupling combinations relevant for leptogenesis are diagonal in the
physical basis where the charged leptons and heavy Majorana neutrinos are
diagonal.Comment: 5 pages; a few comments added; final version to appear in Phys. Rev.
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