Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems

This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that whether and how the thermodynamic structure is invariant in a multiscale stochastic system. That is, whether the relations between thermodynamic functions of state and process variables remain unchanged when the system is viewed at different time scales and resolutions. Our results show that the dynamics on a fast time scale contribute an entropic term to the "internal energy function", $u_S(x)$, for the slow dynamics. Based on the conditional free energy $u_S(x)$, one can then treat the slow dynamics as if the fast dynamics is nonexistent. Furthermore, we show that the free energy, which characterizes the spontaneous organization in a system without detailed balance, is invariant with or without the fast dynamics: The fast dynamics is assumed to reach stationarity instantaneously on the slow time scale; they have no effect on the system's free energy. The same can not be said for the entropy and the internal energy, both of which contain the same contribution from the fast dynamics. We also investigate the consequences of time-scale separation in connection to the concepts of quasi-stationaryty and steady-adiabaticity introduced in the phenomenological steady-state thermodynamics

Deterministic Brownian motion generated from differential delay equations

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.Comment: 15 pages, 13 figure

Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators

Frequency Domain Functional Near-Infrared Spectrometer (fNIRS) for Crew State Monitoring

A frequency domain functional near-infrared spectrometer (fNIRS) and accompanying software have been developed by the NASA Glenn Research Center as part of the Airspace Operations and Safety Program (AOSP) Technologies for Airplane State Awareness (TASA)SE211 Crew State Monitoring (CSM) Project. The goal of CSM was to develop a suite of instruments to measure the cognitive state of operators while performing operational activities. The fNIRS was one of the instruments intended for the CSM, developed to measure changes in oxygen levels in the brain noninvasively

Simple Stellar Population Models as probed by the Large Magellanic Cloud Star Cluster ESO 121-SC03

The presence of blue straggler stars (BSs) in star clusters has proven a challenge to conventional simple stellar population (SSP) models. Conventional SSP models are based on the evolution theory of single stars. Meanwhile, the typical locations of BSs in the colour-magnitude diagram of a cluster are brighter and bluer than the main sequence turn-off point. Such loci cannot be predicted by single-star evolution theory. However, stars with such properties contribute significantly to the integrated light of the cluster. In this paper, we reconstruct the integrated properties of the Large Magellanic Cloud cluster ESO 121-SC03, based on a detailed exploration of the individual cluster stars, and with particular emphasis on the cluster's BSs. We find that the integrated light properties of ESO 121-SC03 are dramatically modified by its BS component. The integrated spectral energy distribution (ISED) flux level is significantly enhanced toward shorter wavelengths, and all broad-band colours become bluer. When fitting the fully integrated ISED of this cluster based on conventional SSP models, the best-fitting values of age and metallicity are significantly underestimated compared to the true cluster parameters. The age underestimate is $\sim40$ per cent if we only include the BSs within the cluster's half-light radius and $\sim60$ per cent if all BSs are included. The corresponding underestimates of the cluster's metallicity are $\sim30$ and $\sim60$ per cent, respectively. The populous star clusters in the Magellanic Clouds are ideal objects to explore the potential importance of BSs for the integrated light properties of more distant unresolved star clusters in a statistically robust manner, since they cover a large range in age and metallicity.Comment: 11 pages, 7 figures, 2 tables, accepted for publication in MNRA

Accuracy of screening tools for Pap smears in general practice

Background: Data extraction tools (DETs) are increasingly being used for research and audit of general practice, despite their limitations. Objective: This study explores the accuracy of Pap smear rates obtained with a DET compared to that of the Pap smear rate obtained with a manual file audit. Method: A widely available DET was used to establish the rate of Pap smears in a large multi-general practice (multi-GP) in regional New South Wales followed by a manual audit of patient files. The main outcome measure was identification of possible discrepancies between the rates established. Results: The DET used significantly underestimated the level of cervical screening compared to the manual audit. In some instances, the patient file contained phone/specialist record of Pap smear conducted elsewhere, which accounted for the failure of the DET to detect some smears. Those patients who had Pap smears whose pathology codes differed between time intervals, i.e. from different pathology providers or from within the same provider but using a different code, were less likely to have had their most recent Pap smear detected by the DET (p \u3c 0.001). Conclusion: Data obtained from DETs should be used with caution as they may not accurately reflect the rate of Pap smears from electronic medical records

Positive-Operator-Valued Time Observable in Quantum Mechanics

We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.Comment: 13 pages, LaTeX, no figures. Some minor changes, expanded the bibliography (now it is bigger than the one in the published version), changed the title and the style for publication on the International Journal of Theoretical Physic