2,274 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
An affine generalization of evacuation
We establish the existence of an involution on tabloids that is analogous to
Schutzenberger's evacuation map on standard Young tableaux. We find that the
number of its fixed points is given by evaluating a certain Green's polynomial
at , and satisfies a "domino-like" recurrence relation.Comment: 32 pages, 7 figure
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
Apodized Pupil Lyot Coronagraphs for Arbitrary Telescope Apertures
In the context of high dynamic range imaging, this study presents a
breakthrough for the understanding of Apodized Pupil Lyot Coronagraphs, making
them available for arbitrary aperture shapes. These new solutions find
immediate application in current, ground-based coronagraphic studies (Gemini,
VLT) and in existing instruments (AEOS Lyot Project). They also offer the
possiblity of a search for an on-axis design for TPF. The unobstructed aperture
case has already been solved by Aime et al. (2002) and Soummer et al. (2003).
Analytical solutions with identical properties exist in the general case and,
in particular, for centrally obscured apertures. Chromatic effects can be
mitigated with a numerical optimization. The combination of analytical and
numerical solutions enables the study of the complete parameter space (central
obstruction, apodization throughput, mask size, bandwidth, and Lyot stop size).Comment: 7 pages 4 figures - ApJL, accepte
Breaking Gender Barriers Through Literature in the Elementary and Pre-School Classroom
The following research assesses how reading and discussing stories that counter gender stereotypes can increase cooperation and decrease conflict between primary- and elementary-aged students of different genders, as well as to expand students’ conceptions of self and others beyond traditional gender expectations. The six-week study involved 50 participants total, 21 between the ages of 3 and 6 and 29 between the ages of 6 and 9 at two separate Montessori public charter schools in Minnesota. Each participant completed an activity pre- and post-intervention concerning the feminine and masculine traits that they would choose to describe themselves and those that could describe someone they’d want to be friends with. 10-minute observations were taken daily to record instances of cooperation and conflict between children of different genders. Pertinent quotes were recorded during observation periods and in discussions about the counter-stereotypical stories. Results showed an increase in the number of friendships between genders, and a greater number of traits chosen to describe selves and potential friends at the elementary school level. Further research in the area is needed to discover the long-term effects of counter-stereotypical literature, the importance of adults examining their own gender biases, and interventions beyond literature to counter patriarchal norms in classrooms
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
Wigner-Yanase skew information as tests for quantum entanglement
A Bell-type inequality is proposed in terms of Wigner-Yanase skew
information, which is quadratic and involves only one local spin observable at
each site. This inequality presents a hierarchic classification of all states
of multipartite quantum systems from separable to fully entangled states, which
is more powerful than the one presented by quadratic Bell inequalities from
two-entangled to fully entangled states. In particular, it is proved that the
inequality provides an exact test to distinguish entangled from nonentangled
pure states of two qubits. Our inequality sheds considerable light on
relationships between quantum entanglement and information theory.Comment: 5 page
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