Symmetry and Symmetry-Breaking in Thermodynamic and Epistemic Engines: A Coupling of First and Second Laws

Abstract

Science traditionally models interactions at the same scale treating systems as isolated first and then as interacting second. This approach has well-recognized limitations. It imputes an original symmetric state space to a system followed by symmetry-breaking operations until systems of a desired order of complexity are reached. Once a level of order is reached they converge back onto their original symmetric state space. This sequential alternation of conservative and nonconservative strategies is tantamount to the assumption that first principles (the First and Second Laws) are so weakly coupled that system dynamics are reversible; hence it assumes the laws operate essentially at the same scale. For systems with complex interiors, where much symmetry-breaking is needed, it is impossible to prevent anomalous modes of organization from arising that inflate the dimensionality of the system—an acknowledged but unavoidable curse of open systems analysis when all parameters are distributed at the same scale (i.e., over the same state space). To prevent this unwelcome outcome, ad hoc algebraic filters or post hoc (super) selection rules must be added to same-scaletheories—a violation of both the parsimony and integrity of the putative first principles. Same-scaletheorists so far have been unable to show how such ad hoc or post hoc provisos may either be avoided, used to formulate new first principles, or to reformulate the old ones. An alternative strategy is to assume that the first principles are coupled nonlinearly rather than linked linearly. The nonlinear strategy assumes that the smallest unit of analysis for explaining complex system dynamics is the nonlinear law-coupleitself, which applies irreversibly across macro-and micro-scales and reversibly across modes at the same scale. Thus symmetry-preserving and symmetry-breaking strategies are treated as a single strategy with no need to postulate theoretically unredeemable provisos. Evidence for the nonlinear coupling of the two laws is found across micro- and macro scales with respect to ascending orders of organization—spaces coupled by geometries, geometries coupled by fields, fields by engines, and engines by systems. These issues are discussed in terms of open complex systems examples (e.g., nest-building by termites, craniofacial growth, perceptual illusions) to illustrate the need for applying the same nonlinearly coupled first principles across the scales of physical, biological, and psychological modes.