On the (Boltzmann) Entropy of Nonequilibrium Systems

Boltzmann defined the entropy of a macroscopic system in a macrostate $M$ as the $\log$ of the volume of phase space (number of microstates) corresponding to $M$. This agrees with the thermodynamic entropy of Clausius when $M$ 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 ${\cal H}$-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 $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi(a) \propto 1/a^{\gamma}$ 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 $q$ 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