First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

Thermodynamic states are assumed to be characterized by densities. Recent ergodic-theory results on the evolution of densities are used to give a unified treatment of the origin of classical nonequilibrium thermodynamic behavior. Asymptotic periodicity is sufficient for the existence of at least one state of (metastable) thermodynamic equilibrium and for the evolution of the entropy to a relative maximum that depends on the way the system is prepared. Ergodicity is necessary and sufficient for a unique state of thermodynamic equilibrium to exist. Exactness, a property of chaotic semidynamical (irreversible) systems, is necessary and sufficient for the global evolution of the entropy to its unique maximum for all initial states. Since all of the laws of physics are formulated as (reversible) dynamical systems, it is unclear why entropy is observed to approach a maximum. Setting aside the possibility that all of the laws of physics are incorrectly formulated, it is demonstrated that either observation of a subset of the complete dynamics (trivial coarse graining) or interactions with an external heat bath (addition of noise) may induce exactness with a consequent evolution of entropy to a maximal state.