2,134 research outputs found
On the (Boltzmann) Entropy of Nonequilibrium Systems
Boltzmann defined the entropy of a macroscopic system in a macrostate as
the of the volume of phase space (number of microstates) corresponding
to . This agrees with the thermodynamic entropy of Clausius when
specifies the locally conserved quantities of a system in local thermal
equilibrium (LTE). Here we discuss Boltzmann's entropy, involving an
appropriate choice of macro-variables, for systems not in LTE. We generalize
the formulas of Boltzmann for dilute gases and of Resibois for hard sphere
fluids and show that for macro-variables satisfying any deterministic
autonomous evolution equation arising from the microscopic dynamics the
corresponding Boltzmann entropy must satisfy an -theorem.Comment: 31 pages, in Tex, authors' e-mails: [email protected],
[email protected]
Illusory Decoherence
If a quantum experiment includes random processes, then the results of
repeated measurements can appear consistent with irreversible decoherence even
if the system's evolution prior to measurement was reversible and unitary. Two
thought experiments are constructed as examples.Comment: 10 pages, 3 figure
Universal efficiency at optimal work with Bayesian statistics
If the work per cycle of a quantum heat engine is averaged over an
appropriate prior distribution for an external parameter , the work becomes
optimal at Curzon-Ahlborn efficiency. More general priors of the form yield optimal work at an efficiency which stays close to
CA value, in particular near equilibrium the efficiency scales as one-half of
the Carnot value. This feature is analogous to the one recently observed in
literature for certain models of finite-time thermodynamics. Further, the use
of Bayes' theorem implies that the work estimated with posterior probabilities
also bears close analogy with the classical formula. These findings suggest
that the notion of prior information can be used to reveal thermodynamic
features in quantum systems, thus pointing to a new connection between
thermodynamic behavior and the concept of information.Comment: revtex4, 5 pages, abstract changed and presentation improved; results
unchanged. New result with Bayes Theorem adde
Information Theory based on Non-additive Information Content
We generalize the Shannon's information theory in a nonadditive way by
focusing on the source coding theorem. The nonadditive information content we
adopted is consistent with the concept of the form invariance structure of the
nonextensive entropy. Some general properties of the nonadditive information
entropy are studied, in addition, the relation between the nonadditivity
and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev.
E(an error in proof of theorem 1 was corrected, typos corrected
Universal Quantum Information Compression
Suppose that a quantum source is known to have von Neumann entropy less than
or equal to S but is otherwise completely unspecified. We describe a method of
universal quantum data compression which will faithfully compress the quantum
information of any such source to S qubits per signal (in the limit of large
block lengths).Comment: RevTex 4 page
A simple formula for pooling knowledge about a quantum system
When various observers obtain information in an independent fashion about a
classical system, there is a simple rule which allows them to pool their
knowledge, and this requires only the states-of-knowledge of the respective
observers. Here we derive an equivalent quantum formula. While its realm of
applicability is necessarily more limited, it does apply to a large class of
measurements, and we show explicitly for a single qubit that it satisfies the
intuitive notions of what it means to pool knowledge about a quantum system.
This analysis also provides a physical interpretation for the trace of the
product of two density matrices.Comment: 5 pages, Revtex
Entanglement reciprocation between qubits and continuous variables
We investigate how entanglement can be transferred between qubits and
continuous variable (CV) systems. We find that one ebit borne in maximally
entangled qubits can be fully transferred to two CV systems which are initially
prepared in pure separable Gaussian field with high excitation. We show that it
is possible, though not straightforward, to retrieve the entanglement back to
qubits from the entangled CV systems. The possibility of deposition of multiple
ebits from qubits to the initially unentangled CV systems is also pointed out.Comment: 4 pages, 3 figures, RevTeX
Incomplete quantum process tomography and principle of maximal entropy
The main goal of this paper is to extend and apply the principle of maximum
entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define
a so-called process entropy function being the von Neumann entropy of the state
associated with the quantum process via Choi-Jamiolkowski isomorphism. It will
be shown that an arbitrary process estimation experiment can be reformulated in
a unified framework and MaxEnt principle can be consistently exploited. We will
argue that the suggested choice for the process entropy satisfies natural list
of properties and it reduces to the state MaxEnt principle, if applied to
preparator devices.Comment: 8 pages, comments welcome, references adde
Combining cosmological datasets: hyperparameters and Bayesian evidence
A method is presented for performing joint analyses of cosmological datasets,
in which the weight assigned to each dataset is determined directly by it own
statistical properties. The weights are considered in a Bayesian context as a
set of hyperparameters, which are then marginalised over in order to recover
the posterior distribution as a function only of the cosmological parameters of
interest. In the case of a Gaussian likelihood function, this marginalisation
may be performed analytically. Calculation of the Bayesian evidence for the
data, with and without the introduction of hyperparameters, enables a direct
determination of whether the data warrant the introduction of weights into the
analysis; this generalises the standard likelihood ratio approach to model
comparison. The method is illustrated by application to the classic toy problem
of fitting a straight line to a set of data. A cosmological illustration of the
technique is also presented, in which the latest measurements of the cosmic
microwave background power spectrum are used to infer constraints on
cosmological parameters.Comment: 12 pages, 6 figures, submitted to MNRA
Autogamy And Inbreeding Depression In Mountain Laurel, Kalmia Latifolia (Ericaceae)
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142278/1/ajb213781.pd
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