Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

Sleep electroencephalogram delta-frequency amplitude, night plasma levels of tumor necrosis factor alpha, and human immunodeficiency virus infection.

We tested the hypothesis that increases in tumor necrosis factor alpha (TNF-alpha) induced by human immunodeficiency virus (HIV) are associated with the increases in slow-wave sleep seen in early HIV infection and the decrease with sleep fragmentation seen in advanced HIV infection. Nocturnal sleep disturbances and associated fatigue contribute to the disability of HIV infection. TNF-alpha causes fatigue in clinical use and promotes slow-wave sleep in animal models. With slow progress toward a vaccine and weak effects from current therapies, efforts are directed toward extending productive life of HIV-infected individuals and shortening the duration of disability in terminal illness. We describe previously unrecognized nocturnal cyclic variations in plasma levels of TNF-alpha in all subjects. In 6 of 10 subjects (1 control subject, 3 HIV-seropositive patients with CD4+ cell number > 400 cells per microliters, and 2 HIV-positive patients with CD4+ cell number < 400 cells per microliters), these fluctuations in TNF-alpha were coupled to the known rhythm of electroencephalogram delta amplitude (square root of power) during sleep. This coupling was not present in 3 HIV-positive subjects with CD4+ cell number < 400 cells per microliters and 1 control subject. In 5 HIV subjects with abnormally low CD4+ cell counts ( < 400 cells per microliters), the number of days since seroconversion correlated significantly with low correlation between TNF-alpha and delta amplitude. We conclude that a previously unrecognized normal, physiological coupling exists between TNF-alpha and delta amplitude during sleep and that the lessened likelihood of this coupling in progressive HIV infection may be important in understanding fatigue-related symptoms and disabilities.