1,037,428 research outputs found
Computability of entropy and information in classical Hamiltonian systems
We consider the computability of entropy and information in classical
Hamiltonian systems. We define the information part and total information
capacity part of entropy in classical Hamiltonian systems using relative
information under a computable discrete partition.
Using a recursively enumerable nonrecursive set it is shown that even though
the initial probability distribution, entropy, Hamiltonian and its partial
derivatives are computable under a computable partition, the time evolution of
its information capacity under the original partition can grow faster than any
recursive function. This implies that even though the probability measure and
information are conserved in classical Hamiltonian time evolution we might not
actually compute the information with respect to the original computable
partition
Optimal Policy with Partial Information in a Forward-Looking Model: Certainty-Equivalence Redux
This paper proves a certainty equivalence result for optimal policy under commitment with symmetric partial information about the state of the economy in a model with forward-looking variables. This result is used in our previous paper, Indicator Variables for Optimal Policy,' which synthesizes what is known about the case of symmetric partial information, and derives useful general formulas for computation of the optimal policy response coefficients and efficient estimates of the state of the economy in the context of a fairly general forward-looking rational-expectations model. In particular, our proof takes into account that, under commitment, the policymaker can affect the future evolution of the observable variables, and thereby potentially affect the future information available.
Variational and Potential Formulation for Stochastic Partial Differential Equations
There is recent interest in finding a potential formulation for Stochastic
Partial Differential Equations (SPDEs). The rationale behind this idea lies in
obtaining all the dynamical information of the system under study from one
single expression. In this Letter we formally provide a general Lagrangian
formalism for SPDEs using the Hojman et al. method. We show that it is possible
to write the corresponding effective potential starting from an s-equivalent
Lagrangean, and that this potential is able to reproduce all the dynamics of
the system, once a special differential operator has been applied. This
procedure can be used to study the complete time evolution and spatial
inhomogeneities of the system under consideration, and is also suitable for the
statistical mechanics description of the problem. Keywords: stochastic partial
differential equations, variational formulation, effective potential. PACS:
45.20.Jj; 02.50.-r; 02.50.Ey.Comment: Letter, 4 pages, no figures; v2: references added, minor change
Retrieving qubit information despite decoherence
The time evolution of a qubit, consisting of two single-level quantum dots,
is studied in the presence of telegraph noise. The dots are connected by two
tunneling paths, with an Aharonov-Bohm flux enclosed between them. Under
special symmetry conditions, which can be achieved by tuning gate voltages,
there develops partial decoherence: at long times, the off-diagonal element of
the reduced density matrix (in the basis of the two dot states) approaches a
non-zero value, generating a circulating current around the loop. The flux
dependence of this current contains full information on the initial quantum
state of the qubit, even at infinite time. Small deviations from this symmetry
yield a very slow exponential decay towards the fully-decoherent limit.
However, the amplitudes of this decay also contain the full information on the
initial qubit state, measurable either via the current or via the occupations
of the qubit dots.Comment: 10 pages, 4 figure
Local Tomography of Large Networks under the Low-Observability Regime
This article studies the problem of reconstructing the topology of a network
of interacting agents via observations of the state-evolution of the agents. We
focus on the large-scale network setting with the additional constraint of
observations, where only a small fraction of the agents can be
feasibly observed. The goal is to infer the underlying subnetwork of
interactions and we refer to this problem as . In order to
study the large-scale setting, we adopt a proper stochastic formulation where
the unobserved part of the network is modeled as an Erd\"{o}s-R\'enyi random
graph, while the observable subnetwork is left arbitrary. The main result of
this work is establishing that, under this setting, local tomography is
actually possible with high probability, provided that certain conditions on
the network model are met (such as stability and symmetry of the network
combination matrix). Remarkably, such conclusion is established under the
- , where the cardinality of the observable
subnetwork is fixed, while the size of the overall network scales to infinity.Comment: To appear in IEEE Transactions on Information Theor
Quantum Dynamical Approach of Wavefunction Collapse in Measurement Process and Its Application to Quantum Zeno Effect
The systematical studies on the dynamical approach of wavefunction collapse
in quantum measurement are reported in this paper based on the Hepp-Coleman's
model and its generalizations. Under certain physically reasonable conditions,
which are easily satisfied by the practical problems, it is shown that the
off-diagonal elements of the reduced density matrix vanish in quantum
mechanical evolution process in the macroscopic limit with a very large
particle number N. Various examples with detector made up of oscillators of
different spectrum distribution are used to illustrate this observations . With
the two-level system as an explicit illustration, the quantum information
entropy is exactly obtained to quantitatively describe the degree of
decoherence for the so-called partial coherence caused by detector. The entropy
for the case with many levels is computed based on perturbation method in the
limits with very large and very small N. As an application of this general
approach for quantum measurement, a dynamical realization of the quantum Zeno
effect are present to analyse its recent testing experiment in connection with
a description of transition in quantum information entropy. Finally, the Cini's
model for the correlation between the states of the measured system and the
detector is generalized for the case with many energy-level.Comment: ITP.SUNYSB preprint Sep.,199
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