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

Current physics faces four core challenges: the unification dilemma of general relativity and quantum mechanics, the nature of dark matter and dark energy, the non-locality of quantum entanglement, and the cosmic singularity paradox. Traditional non-equilibrium field theory struggles to balance the cooperative evolution of topological structures and quantum coherence when describing emergent phenomena in complex systems. Based on the vacuum quantum fluctuation ontology of π-cosmology theory, this paper constructs a self-consistent and falsifiable non-equilibrium quantum field theory framework: 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 speculate that the total cosmic coherence {Cₓ₎ₓ₀₋} is strictly conserved, with the transfer and transformation of local coherent order dominating the evolution of complex systems; Starting from the path integral of the λ-field, derive the topological order parameter {C⏚} through the renormalization group flow equation, prove its objective reality as an eigenvalue of the field theory equation, and explain the topological phase transition nature of hierarchical transitions in complex systems; Redefine the physical connotations of energy and mass, introduce coherence energy gap as a new physical quantity, provide a specific numerical range for the prediction of "mass deficit in living organisms", correlate with existing Superconducting Quantum Interference Device (SQUID) technology, and provide a clear and falsifiable experimental path; Introduce the topological protection edge state argument to explain the "concealment" 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 coherent order in complex systems. Its validity depends on the experimental verification of mass differences of specific magnitudes, providing 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. )