11,789 research outputs found
Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
We show why the amount of information communicated between the past and
future--the excess entropy--is not in general the amount of information stored
in the present--the statistical complexity. This is a puzzle, and a
long-standing one, since the latter is what is required for optimal prediction,
but the former describes observed behavior. We layout a classification scheme
for dynamical systems and stochastic processes that determines when these two
quantities are the same or different. We do this by developing closed-form
expressions for the excess entropy in terms of optimal causal predictors and
retrodictors--the epsilon-machines of computational mechanics. A process's
causal irreversibility and crypticity are key determining properties.Comment: 4 pages, 2 figure
Telling time with an intrinsically noisy clock
Intracellular transmission of information via chemical and transcriptional
networks is thwarted by a physical limitation: the finite copy number of the
constituent chemical species introduces unavoidable intrinsic noise. Here we
provide a method for solving for the complete probabilistic description of
intrinsically noisy oscillatory driving. We derive and numerically verify a
number of simple scaling laws. Unlike in the case of measuring a static
quantity, response to an oscillatory driving can exhibit a resonant frequency
which maximizes information transmission. Further, we show that the optimal
regulatory design is dependent on the biophysical constraints (i.e., the
allowed copy number and response time). The resulting phase diagram illustrates
under what conditions threshold regulation outperforms linear regulation.Comment: 10 pages, 5 figure
A General Information Theoretical Proof for the Second Law of Thermodynamics
We show that the conservation and the non-additivity of the information,
together with the additivity of the entropy make the entropy increase in an
isolated system. The collapse of the entangled quantum state offers an example
of the information non-additivity. Nevertheless, the later is also true in
other fields, in which the interaction information is important. Examples are
classical statistical mechanics, social statistics and financial processes. The
second law of thermodynamics is thus proven in its most general form. It is
exactly true, not only in quantum and classical physics but also in other
processes, in which the information is conservative and non-additive.Comment: 4 page
Near-Extreme Black Holes and the Universal Relaxation Bound
A fundamental bound on the relaxation time \tau of a perturbed
thermodynamical system has recently been derived, \tau \geq \hbar/\pi T, where
is the system's temperature. We demonstrate analytically that black holes
saturate this bound in the extremal limit and for large values of the azimuthal
number m of the perturbation field.Comment: 2 Pages. Submitted to PRD on 5/12/200
Measuring the effective complexity of cosmological models
We introduce a statistical measure of the effective model complexity, called
the Bayesian complexity. We demonstrate that the Bayesian complexity can be
used to assess how many effective parameters a set of data can support and that
it is a useful complement to the model likelihood (the evidence) in model
selection questions. We apply this approach to recent measurements of cosmic
microwave background anisotropies combined with the Hubble Space Telescope
measurement of the Hubble parameter. Using mildly non-informative priors, we
show how the 3-year WMAP data improves on the first-year data by being able to
measure both the spectral index and the reionization epoch at the same time. We
also find that a non-zero curvature is strongly disfavored. We conclude that
although current data could constrain at least seven effective parameters, only
six of them are required in a scheme based on the Lambda-CDM concordance
cosmology.Comment: 9 pages, 4 figures, revised version accepted for publication in PRD,
updated with WMAP3 result
Lossless quantum data compression and variable-length coding
In order to compress quantum messages without loss of information it is
necessary to allow the length of the encoded messages to vary. We develop a
general framework for variable-length quantum messages in close analogy to the
classical case and show that lossless compression is only possible if the
message to be compressed is known to the sender. The lossless compression of an
ensemble of messages is bounded from below by its von-Neumann entropy. We show
that it is possible to reduce the number of qbits passing through a quantum
channel even below the von-Neumann entropy by adding a classical side-channel.
We give an explicit communication protocol that realizes lossless and
instantaneous quantum data compression and apply it to a simple example. This
protocol can be used for both online quantum communication and storage of
quantum data.Comment: 16 pages, 5 figure
An Information--Theoretic Equality Implying the Jarzynski Relation
We derive a general information-theoretic equality for a system undergoing
two projective measurements separated by a general temporal evolution. The
equality implies the non-negativity of the mutual information between the
measurement outcomes of the earlier and later projective measurements. We show
that it also contains the Jarzynski relation between the average exponential of
the thermodynamical work and the exponential of the difference between the
initial and final free energy. Our result elucidates the information-theoretic
underpinning of thermodynamics and explains why the Jarzynski relation holds
identically both quantumly as well as classically.Comment: 2 pages, no figure
Fluctuation Theorem with Information Exchange: Role of Correlations in Stochastic Thermodynamics
We establish the fluctuation theorem in the presence of information exchange
between a nonequilibrium system and other degrees of freedom such as an
observer and a feedback controller, where the amount of information exchange is
added to the entropy production. The resulting generalized second law sets the
fundamental limit of energy dissipation and energy cost during the information
exchange. Our results apply not only to feedback-controlled processes but also
to a much broader class of information exchanges, and provides a unified
framework of nonequilibrium thermodynamics of measurement and feedback control.Comment: To appear in PR
Information-theory-based solution of the inverse problem in classical statistical mechanics
We present a procedure for the determination of the interaction potential
from the knowledge of the radial pair distribution function. The method,
realized inside an inverse Monte Carlo simulation scheme, is based on the
application of the Maximum Entropy Principle of information theory and the
interaction potential emerges as the asymptotic expression of the transition
probability. Results obtained for high density monoatomic fluids are very
satisfactory and provide an accurate extraction of the potential, despite a
modest computational effort.Comment: 9 pages, 2 figure
Quantum Entanglement of Moving Bodies
We study the properties of quantum information and quantum entanglement in
moving frames. We show that the entanglement between the spins and the momenta
of two particles can be interchanged under a Lorentz transformation, so that a
pair of particles that is entangled in spin but not momentum in one reference
frame, may, in another frame, be entangled in momentum at the expense of
spin-entanglement. Similarly, entanglement between momenta may be transferred
to spin under a Lorentz transformation. While spin and momentum entanglement
each is not Lorentz invariant, the joint entanglement of the wave function is.Comment: 4 pages, 2 figures. An error was corrected in the numerical data and
hence the discussion of the data was changed. Also, references were added.
Another example was added to the pape
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