A Generalised Theory of Interactions -- II. The Theoretical Construction

Abstract

After discussing the significance of interactions to understand complex multiscale stochastic systems (CMSS), we turn our attention to the construction of a Generalised Theory of Interactions (GToI). We define interactions as discrete, localised events where the thermodynamically irreversible exchange of degrees of freedom involves signal propagation and relaxation phenomena. We proceed to define the mechanics of such space, as well as how these approximately map onto dynamical manifolds. By characterising various systems through the effect of transformations across interaction space, we develop a view of systems where features such as emergence and information representation become apparent. Our theory appears to capture structural and dynamical features of CMSS efficiently by making explicit the extent of the dynamical range of action in them; we identify the boundaries of such range with statistical limits corresponding to physical laws, and derive a generalised form of the Correspondence Principle.