Consistency of the Shannon entropy in quantum experiments

The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.Comment: 12 pages, LaTeX2e/REVTeX4. V5: slightly different than the published versio

Evolution of Liouville density of a chaotic system

An area-preserving map of the unit sphere, consisting of alternating twists and turns, is mostly chaotic. A Liouville density on that sphere is specified by means of its expansion into spherical harmonics. That expansion initially necessitates only a finite number of basis functions. As the dynamical mapping proceeds, it is found that the number of non-negligible coefficients increases exponentially with the number of steps. This is to be contrasted with the behavior of a Schr\"odinger wave function which requires, for the analogous quantum system, a basis of fixed size.Comment: LaTeX 4 pages (27 kB) followed by four short PostScript files (2 kB + 2 kB + 1 kB + 4 kB

Chaos and quantum-nondemolition measurements

The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ‘‘deterministic randomness’’ in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity

INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION

It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at [email protected] (internet)

Chaotic Evolution in Quantum Mechanics

A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure

Muscle-specific deletion of SOCS3 increases the early inflammatory response but does not affect regeneration after myotoxic injury

Myosin heavy chain gene expression and muscle fiber oxidative capacity in muscles from uninjured control and SOCS3 MKO mice. qRT-PCR using primers to detect MyHCIIb (A), MyHCIIx (B), MyHCI (C), and MyHCIIa (D) was performed on RNA extracted from snap frozen muscles following dissection. Data are expressed as mean ± SEM and compared with an unpaired two-tailed Student’s t test. n = 8 mice/genotype. (E) Representative succinate dehydrogenase (SDH)-reacted TA muscle sections from uninjured muscles of 12-week-old control and SOCS3 MKO mice. Quantification of SDH intensity was determined by analysis of SDH reacted TA muscle sections. Data are expressed as mean ± SEM and compared with an unpaired two-tailed Student’s t test. n = 5 mice/genotype. Scale bar = 100 μm. (PDF 145 kb

Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.Comment: 10 pages, Latex2e file, references added, minor clarifications mad

Are some children genetically predisposed to poor sleep? A polygenic risk study in the general population

Background: Twin studies show moderate heritability of sleep traits: 40% for insomnia symptoms and 46% for sleep duration. Genome-wide association studies (GWAS) have identified genetic variants involved in insomnia and sleep duration in adults, but it is unknown whether these variants affect sleep during early development. We assessed whether polygenic risk scores for insomnia (PRS-I) and sleep duration (PRS-SD) affect sleep throughout early childhood to adolescence. Methods: We included 2,458 children of European ancestry (51% girls). Insomnia-related items of the Child Behavior Checklist were reported by mothers at child's age 1.5, 3, and 6 years. At 10–15 years, the Sleep Disturbance Scale for Children and actigraphy were assessed in a subsample (N = 975). Standardized PRS-I and PRS-SD (higher scores indicate genetic susceptibility for insomnia and longer sleep duration, respectively) were computed at multiple p-value thresholds based on largest GWAS to date. Results: Children with higher PRS-I had more insomnia-related sleep problems between 1.5 and 15 years (BPRS-I &lt; 0.001 =.09, 95% CI: 0.05; 0.14). PRS-SD was not associated with mother-reported sleep problems. A higher PRS-SD was in turn associated with longer actigraphically estimated sleep duration (BPRS-SD &lt; 5e08 =.05, 95% CI: 0.001; 0.09) and more wake after sleep onset (BPRS-SD &lt; 0.005 =.25, 95% CI: 0.04; 0.47) at 10–15 years, but these associations did not survive multiple testing correction. Conclusions: Children who are genetically predisposed to insomnia have more insomnia-like sleep problems, whereas those who are genetically predisposed to longer sleep have longer sleep duration, but are also more awake during the night in adolescence. This indicates that polygenic risk for sleep traits, based on GWAS in adults, affects sleep already in children.</p