A phenomenological calculus for complex systems

摘要: Abstract The difficulties in framing and solving dynamical equations encompassing the detailed interactions of complex biological systems are legion. As an alternative to comprehensive system dynamics, a calculus is derived which phenomenologically relates generalized causes their resultant effects. A divided into distinct, interacting subsystems, indexed by i. force (affector or cause) upon any subsystem given vector Fi. constitutive properties ai. It postulated that response set imposed forces {Fi} dyadic R ≡aiFi (Einstein summation) called tensor. There many ways describe dynamics this manner, it invariant under such transformations. This analogous invariance radius = eixi co-ordinate Using techniques metric geometry, shown these simple postulates lead phenomenological with structure similar irreversible thermodynamics (a special case calculus). In particular, if {ai} {Ji} belong space dual {Fi}, then Ji LijFj, where Lij ai elements gives canonical relationship between (or causes) fluxes effects), denoted Ji. By definition, Lji. Furthermore, there principle directionality: ¦ ¦2≡ : LijFi. Fi≥0. thermodynamics, simply Second Law: ¦2 δ ≥ 0, dissipation function. What remarkable, positive-definite condition results from defining tensor not assumed as physical law. paper ends discussion applying problems aging.