1,715 research outputs found
A Schroedinger link between non-equilibrium thermodynamics and Fisher information
It is known that equilibrium thermodynamics can be deduced from a constrained
Fisher information extemizing process. We show here that, more generally, both
non-equilibrium and equilibrium thermodynamics can be obtained from such a
Fisher treatment. Equilibrium thermodynamics corresponds to the ground state
solution, and non-equilibrium thermodynamics corresponds to excited state
solutions, of a Schroedinger wave equation (SWE). That equation appears as an
output of the constrained variational process that extremizes Fisher
information. Both equilibrium- and non-equilibrium situations can thereby be
tackled by one formalism that clearly exhibits the fact that thermodynamics and
quantum mechanics can both be expressed in terms of a formal SWE, out of a
common informational basis.Comment: 12 pages, no figure
Power laws of complex systems from Extreme physical information
Many complex systems obey allometric, or power, laws y=Yx^{a}. Here y is the
measured value of some system attribute a, Y is a constant, and x is a
stochastic variable. Remarkably, for many living systems the exponent a is
limited to values +or- n/4, n=0,1,2... Here x is the mass of a randomly
selected creature in the population. These quarter-power laws hold for many
attributes, such as pulse rate (n=-1). Allometry has, in the past, been
theoretically justified on a case-by-case basis. An ultimate goal is to find a
common cause for allometry of all types and for both living and nonliving
systems. The principle I - J = extrem. of Extreme physical information (EPI) is
found to provide such a cause. It describes the flow of Fisher information J =>
I from an attribute value a on the cell level to its exterior observation y.
Data y are formed via a system channel function y = f(x,a), with f(x,a) to be
found. Extremizing the difference I - J through variation of f(x,a) results in
a general allometric law f(x,a)= y = Yx^{a}. Darwinian evolution is presumed to
cause a second extremization of I - J, now with respect to the choice of a. The
solution is a=+or-n/4, n=0,1,2..., defining the particular powers of biological
allometry. Under special circumstances, the model predicts that such biological
systems are controlled by but two distinct intracellular information sources.
These sources are conjectured to be cellular DNA and cellular transmembrane ion
gradient
Fisher information, Wehrl entropy, and Landau Diamagnetism
Using information theoretic quantities like the Wehrl entropy and Fisher's
information measure we study the thermodynamics of the problem leading to
Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic
field. It is shown that such a problem can be "translated" into that of the
thermal harmonic oscillator. We discover a new Fisher-uncertainty relation,
derived via the Cramer-Rao inequality, that involves phase space localization
and energy fluctuations.Comment: no figures. Physical Review B (2005) in pres
Multi-Frequency Synthesis of VLBI Images Using a Generalized Maximum Entropy Method
A new multi-frequency synthesis algorithm for reconstructing images from
multi-frequency VLBI data is proposed. The algorithm is based on a generalized
maximum-entropy method, and makes it possible to derive an effective spectral
correction for images over a broad frequency bandwidth, while simultaneously
reconstructing the spectral-index distribution over the source. The results of
numerical simulations demonstrating the capabilities of the algorithm are
presented.Comment: 17 pages, 8 figure
Quantum theory of incompatible observations
Maximum likelihood principle is shown to be the best measure for relating the
experimental data with the predictions of quantum theory.Comment: 3 page
Delocalization and the semiclassical description of molecular rotation
We discuss phase-space delocalization for the rigid rotator within a
semiclassical context by recourse to the Husimi distributions of both the
linear and the anisotropic instances. Our treatment is based upon the
concomitant Fisher information measures. The pertinent Wehrl entropy is also
investigated in the linear case.Comment: 6 pages, 3 figure
Reconstructing Images from Projections Using the Maximum-Entropy Method. Numerical Simulations of Low-Aspect Astrotomography
The reconstruction of images from a small number of projections using the
maximum-entropy method (MEM) with the Shannon entropy is considered. MEM
provides higher-quality image reconstruction for sources with extended
components than the Hogbom CLEAN method, which is also used in low-aspect
astrotomography. The quality of image reconstruction for sources with mixed
structure containing bright, compact features embedded in a comparatively weak,
extended base can be further improved using a difference-mapping method, which
requires a generalization of MEM for the reconstruction of sign-variable
functions.We draw conclusions based on the results of numerical simulations for
a number of model radio sources with various morphologies.Comment: 11 pages, 9 figure
Continuous variable entanglement distillation of Non-Gaussian Mixed States
Many different quantum information communication protocols such as
teleportation, dense coding and entanglement based quantum key distribution are
based on the faithful transmission of entanglement between distant location in
an optical network. The distribution of entanglement in such a network is
however hampered by loss and noise that is inherent in all practical quantum
channels. Thus, to enable faithful transmission one must resort to the protocol
of entanglement distillation. In this paper we present a detailed theoretical
analysis and an experimental realization of continuous variable entanglement
distillation in a channel that is inflicted by different kinds of non-Gaussian
noise. The continuous variable entangled states are generated by exploiting the
third order non-linearity in optical fibers, and the states are sent through a
free-space laboratory channel in which the losses are altered to simulate a
free-space atmospheric channel with varying losses. We use linear optical
components, homodyne measurements and classical communication to distill the
entanglement, and we find that by using this method the entanglement can be
probabilistically increased for some specific non-Gaussian noise channels
Dynamics of the Fisher Information Metric
We present a method to generate probability distributions that correspond to
metrics obeying partial differential equations generated by extremizing a
functional , where is the
Fisher metric. We postulate that this functional of the dynamical variable
is stationary with respect to small variations of these
variables. Our approach enables a dynamical approach to Fisher information
metric. It allows to impose symmetries on a statistical system in a systematic
way. This work is mainly motivated by the entropy approach to nonmonotonic
reasoning.Comment: 11 page
A Solution to the Problem of Phaseless Mapping for a High-Orbit Space-Ground Radio Interferometer
We consider the problem of mapping with ultra-high angular resolution using a
space-ground radio interferometer with a space antenna in a high orbit,whose
apogee height exceeds the radius of the Earth by a factor of ten. In this case,
a multielement interferometer essentially degenerates into a two-element
interferometer. The degeneracy of the close-phase relations prevents the use of
standard methods for hybrid mapping and self-calibration for the correct
reconstruction of images. We propose a new phaseless mapping method based on
methods for the reconstruction of images in the complete absence of phase
information, using only the amplitudes of the spatial-coherence function of the
source. In connection with this problem, we propose a new method for the
reliable solution of the phase problem, based on optimizing
information-carrying nonlinear functionals, in particular, the Shannon entropy.
Results of simulations of mapping radio sources with various structures with
ultra-high angular resolution in the framework of the RADIOASTRON mission are
presented.Comment: 15 pages, 7 figure
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