π-Universe Theory Non-Equilibrium Quantum Field Theory and Emergent Phenomena in Complex Systems

Abstract: Current physics faces four core challenges: the unification dilemma of general relativity and quantum mechanics, the nature of dark matter and dark energy, the nonlocality of quantum entanglement, and the cosmic singularity paradox. Traditional non-equilibrium field theory struggles to balance the coordinated evolution of topological structure and quantum coherence when describing emergent phenomena in complex systems. Based on the vacuum quantum fluctuation ontology of π-Universe theory, this paper constructs a self-consistent and falsifiable non-equilibrium quantum field theory framework: 1. Propose the Law of Coherence Conservation as a supplement to expand the applicable boundary of the traditional second law of thermodynamics in non-equilibrium systems, and infer that the total global coherence of the universe is strictly conserved, where the transfer and transformation of local coherence order dominate the evolution of complex systems; 2. Derive the topological order parameter from the path integral of the λ-field through the renormalization group flow equation, prove its objective reality as an eigenvalue of the field theory equation, and explain the essential nature of topological phase transitions in the hierarchical transition of complex systems; 3. Redefine the physical connotations of energy and mass, introduce thecoherence energy gap as a new physical quantity, provide a specific numerical value for the prediction of "mass deficit in living organisms", correlate with existing Superconducting Quantum Interference Device (SQUID) technology, and offer a clear and falsifiable experimental path; 4. Introduce the argument of topologically protected edge states to explain the "invisibility" of the λ-field in past experiments and illustrate its physical characteristics as a low-energy non-perturbative topological effect. This theory provides a possible explanatory framework that can describe the non-Markovian dynamics of high-order coherence order in complex systems, whose validity depends on the experimental verification of mass differences at a specific order of magnitude, thereby offering a new perspective for the research of non-equilibrium quantum field theory and complex systems.(A full Chinese version of this work is included as an additional file.)