1,206 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
Information-theoretic significance of the Wigner distribution
A coarse grained Wigner distribution p_{W}(x,u) obeying positivity derives
out of information-theoretic considerations. Let p(x,u) be the unknown joint
PDF (probability density function) on position- and momentum fluctuations x,u
for a pure state particle. Suppose that the phase part Psi(x,z) of its Fourier
transform F.T.[p(x,u)]=|Z(x,z)|exp[iPsi(x,z)] is constructed as a hologram.
(Such a hologram is often used in heterodyne interferometry.) Consider a
particle randomly illuminating this phase hologram. Let its two position
coordinates be measured. Require that the measurements contain an extreme
amount of Fisher information about true position, through variation of the
phase function Psi(x,z). The extremum solution gives an output PDF p(x,u) that
is the convolution of the Wigner p_{W}(x,u) with an instrument function
defining uncertainty in either position x or momentum u. The convolution arises
naturally out of the approach, and is one-dimensional, in comparison with the
two-dimensional convolutions usually proposed for coarse graining purposes. The
output obeys positivity, as required of a PDF, if the one-dimensional
instrument function is sufficiently wide. The result holds for a large class of
systems: those whose amplitudes a(x) are the same at their boundaries
(Examples: states a(x) with positive parity; with periodic boundary conditions;
free particle trapped in a box).Comment: pdf version has 16 pages. No figures. Accepted for publ. in PR
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's arrow of `time' in cosmological coherent phase space
Fisher's arrow of `time' in a cosmological phase space defined as in quantum
optics (i.e., whose points are coherent states) is introduced as follows.
Assuming that the phase space evolution of the universe starts from an initial
squeezed cosmological state towards a final thermal one, a Fokker-Planck
equation for the time-dependent, cosmological Q phase space probability
distribution can be written down. Next, using some recent results in the
literature, we derive an information arrow of time for the Fisher phase space
cosmological entropy based on the Q function. We also mention the application
of Fisher's arrow of time to stochastic inflation modelsComment: 10 pages, LaTex, Honorable Mention at GRF-199
Signal transmission through elements of the cytoskeleton form an optimized information network in eukaryotic cells
Multiple prior empirical and theoretical studies have demonstrated wire-like flow of electrons and ions along elements of the cytoskeleton but this has never been linked to a biological function. Here we propose that eukaryotes use this mode of signal transmission to convey spatial and temporal environmental information from the cell membrane to the nucleus. The cell membrane, as the interface between intra-and extra-cellular environments, is the site at which much external information is received. Prior studies have demonstrated that transmembrane ion gradients permit information acquisition when an environmental signal interacts with specialized protein gates in membrane ion channels and producing specific ions to flow into or out of the cell along concentration gradients. The resulting localized change in cytoplasmic ion concentrations and charge density can alter location and enzymatic function of peripheral membrane proteins. This allows the cell to process the information and rapidly deploy a local response. Here we investigate transmission of information received and processed in and around the cell membrane by elements of the cytoskeleton to the nucleus to alter gene expression. We demonstrate signal transmission by ion flow along the cytoskeleton is highly optimized. In particular, microtubules, with diameters of about 30 nm, carry coarse-grained Shannon information to the centrosome adjacent to the nucleus with minimum loss of input source information. And, microfilaments, with diameters of about 4 nm, transmit maximum Fisher (fine-grained) information to protein complexes in the nuclear membrane. These previously unrecognized information dynamics allow continuous integration of spatial and temporal environmental signals with inherited information in the genome.National Cancer Institute Physical Science Oncology Center [U54 CA143970]; NCI CCSG Support Grant [P30 CA076292]Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]
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
Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature
Frieden and Soffer conjectured some years ago the existence of a ``Fisher
temperature" T_F that would play, with regards to Fisher's information measure
I, the same role that the ordinary temperature T plays vis-a-vis Shannon's
logarithmic measure. Here we exhibit the existence of reciprocity relations
between T_F and T and provide an interpretation with reference to the meaning
of T_F for the canonical ensemble.Comment: 3 pages, no figure
- …