276 research outputs found
MaxEnt and dynamical information
The MaxEnt solutions are shown to display a variety of behaviors (beyond the
traditional and customary exponential one) if adequate dynamical information is
inserted into the concomitant entropic-variational principle. In particular, we
show both theoretically and numerically that power laws and power laws with
exponential cut-offs emerge as equilibrium densities in proportional and other
dynamics
Illusory Decoherence
If a quantum experiment includes random processes, then the results of
repeated measurements can appear consistent with irreversible decoherence even
if the system's evolution prior to measurement was reversible and unitary. Two
thought experiments are constructed as examples.Comment: 10 pages, 3 figure
Statistical mechanics in the context of special relativity
In the present effort we show that is the unique existing entropy obtained
by a continuous deformation of the Shannon-Boltzmann entropy and preserving unaltered its fundamental properties of concavity,
additivity and extensivity. Subsequently, we explain the origin of the
deformation mechanism introduced by and show that this deformation
emerges naturally within the Einstein special relativity. Furthermore, we
extend the theory in order to treat statistical systems in a time dependent and
relativistic context. Then, we show that it is possible to determine in a self
consistent scheme within the special relativity the values of the free
parameter which results to depend on the light speed and reduces
to zero as recovering in this way the ordinary statistical
mechanics and thermodynamics. The novel statistical mechanics constructed
starting from the above entropy, preserves unaltered the mathematical and
epistemological structure of the ordinary statistical mechanics and is suitable
to describe a very large class of experimentally observed phenomena in low and
high energy physics and in natural, economic and social sciences. Finally, in
order to test the correctness and predictability of the theory, as working
example we consider the cosmic rays spectrum, which spans 13 decades in energy
and 33 decades in flux, finding a high quality agreement between our
predictions and observed data.
PACS number(s): 05.20.-y, 51.10.+y, 03.30.+p, 02.20.-aComment: 17 pages (two columns), 5 figures, RevTeX4, minor typing correction
Mesoscopic transport beyond linear response
We present an approach to steady-state mesoscopic transport based on the
maximum entropy principle formulation of nonequilibrium statistical mechanics.
Our approach is not limited to the linear response regime. We show that this
approach yields the quantization observed in the integer quantum Hall effect at
large currents, which until now has been unexplained. We also predict new
behaviors of non-local resistances at large currents in the presence of dirty
contacts.Comment: 14 pages plus one figure (with an insert) (post-script codes
appended), RevTeX 3.0, UCF-CM-93-004 (Revised
Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
A new information-geometric approach to chaotic dynamics on curved
statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown
that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical
manifold M_{s} underlying an ED Gaussian model describing an arbitrary system
of 3N degrees of freedom leads to linear information-geometric entropy growth
and to exponential divergence of the Jacobi vector field intensity, quantum and
classical features of chaos respectively.Comment: 8 pages, final version accepted for publicatio
Variational Principle underlying Scale Invariant Social Systems
MaxEnt's variational principle, in conjunction with Shannon's logarithmic
information measure, yields only exponential functional forms in
straightforward fashion. In this communication we show how to overcome this
limitation via the incorporation, into the variational process, of suitable
dynamical information. As a consequence, we are able to formulate a somewhat
generalized Shannonian Maximum Entropy approach which provides a unifying
"thermodynamic-like" explanation for the scale-invariant phenomena observed in
social contexts, as city-population distributions. We confirm the MaxEnt
predictions by means of numerical experiments with random walkers, and compare
them with some empirical data
Distribution of the daily Sunspot Number variation for the last 14 solar cycles
The difference between consecutive daily Sunspot Numbers was analysed. Its
distribution was approximated on a large time scale with an exponential law. In
order to verify this approximation a Maximum Entropy distribution was generated
by a modified version of the Simulated Annealing algorithm. The exponential
approximation holds for the generated distribution too. The exponential law is
characteristic for time scales covering whole cycles and it is mostly a
characteristic of the Sunspot Number fluctuations and not of its average
variation.Comment: Accepted for publication in Solar Physic
Observables suitable for restricting the fidelity to multipartite maximally entangled states
We present a class of observables which are suitable for determining the
fidelity of a state to the multipartite Greenberger-Horne-Zeilinger (GHZ)
state. Given an expectation value of an observable belonging to the class, we
give a simple formula that gives a lower bound and an upper bound for the
fidelity. Applying the formula to the GHZ-state preparation experiment by Pan
{\it et al}. {[Nature (London) {\bf 403}, 515 (2000)]}, we show that the
observed state lies outside of the class of biseparable mixed three-qubit
states. We also show that for this class of operators, adopting the principle
of minimum variance {[Phys. Rev. A {\bf 60}, 4338 (1999)]} in the state
estimation always results in the state with the minimum fidelity.Comment: 6 page
Quantum Bayes rule
We state a quantum version of Bayes's rule for statistical inference and give
a simple general derivation within the framework of generalized measurements.
The rule can be applied to measurements on N copies of a system if the initial
state of the N copies is exchangeable. As an illustration, we apply the rule to
N qubits. Finally, we show that quantum state estimates derived via the
principle of maximum entropy are fundamentally different from those obtained
via the quantum Bayes rule.Comment: REVTEX, 9 page
The maximum entropy formalism and the idiosyncratic theory of biodiversity
Why does the neutral theory, which is based on unrealistic assumptions, predict diversity patterns so accurately? Answering questions like this requires a radical change in the way we tackle them. The large number of degrees of freedom of ecosystems pose a fundamental obstacle to mechanistic modelling. However, there are tools of statistical physics, such as the maximum entropy formalism (MaxEnt), that allow transcending particular models to simultaneously work with immense families of models with different rules and parameters, sharing only well-established features. We applied MaxEnt allowing species to be ecologically idiosyncratic, instead of constraining them to be equivalent as the neutral theory does. The answer we found is that neutral models are just a subset of the majority of plausible models that lead to the same patterns. Small variations in these patterns naturally lead to the main classical species abundance distributions, which are thus unified in a single framework
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