Stochastic mechanics in the context of the properties of living systems

Many features of living systems prevent application of fundamental statistical mechanics (FSM) to study these systems. The present work focuses on some of these features. By discussing all the basic approaches of FSM, the work formulates the extension of the kinetic-theory paradigm (based on the reduced one-particle distribution function) that exhibits all of the considered properties of living systems. This extension appears to be a model within the generalized-kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. A mathematical formulation of homeorhesis is also derived. An example discussed in the work is a generalized kinetic equation coupled with the probabilitydensity equation representing the varying component content of a living system. The work also suggests a few directions for future research.