A dynamical field theory for dissipative systems: The hierarchical structure of field thermodynamics

Abstract

The analytical exploration of hierarchical structures is a central problem in modern biology. In many ways, the most basic tenet of any theory of any biological system is that its behavior lies within the laws of thermodynamics. Thus an investigation into the hierarchical structure of field thermodynamics is in effect an investigation into the underlying structures common to all biological systems. In field thermodynamics, the dynamics is prescribed at the hierarchical level of description concerned with the motions of classes of the various molecular species flowing in the system. Of crucial importance are scale factors which convert potentials into potential energies per mole of the various molecular species. On the other hand, the overall behavior of the system is presented at a higher hierarchical level of description in terms of systemic properties such as charge density or entropy density. Three questions are investigated: (1) how is the transition from the specific to the systemic level of description effected, (2) given the scale factors at the specific level how does one find those at the systemic level, and (3) what relationship can one find between the scale factors at the two levels of description? Answering these questions necessitates an examination of the nature of the forces at the two levels of the hierarchy of descriptions.