Physiology and Homeostasis: Cellular Communication and Multicellular Regulation—Volume IV of the Axiomatization of Biology in the Global-Realism Framework

This manuscript develops the fourth biological volume of the global-realist axiomatization program by deriving multicellular communication and physiological regulation from the established physical, chemical, cellular, genetic, and metabolic layers. Nerve impulses, synapses, hormones, endocrine axes, muscle force, cardiac pumping, immune recognition, and homeostasis are not admitted as primitive explanatory terms. Excitable membranes are defined as capacitive ionic interfaces with state-dependent molecular conductances, while action potentials are derived as regenerative traveling pulses of the resulting reaction–diffusion system. Chemical synaptic transmission is constructed from voltage sensing, calcium entry, cooperative vesicle fusion, diffusion, receptor recognition, and transmitter clearance. Endocrine signaling is formulated through advection–diffusion–reaction transport, receptor occupancy, bounded intracellular gain, and delayed negative feedback. Muscle contraction is derived from ATP-driven cross-bridge Markov cycles, filament-overlap geometry, calcium conservation, and active-tension dynamics. Cardiac output and vascular delivery follow from pressure–volume work, valved chamber mechanics, fluid dynamics, vascular resistance, compliance, network conservation, capillary filtration, and lymphatic return. Immunity is reconstructed as contextual molecular decision-making involving recognition free energies, complement regulation, somatic receptor recombination, peptide–MHC presentation, tolerance filtering, clonal selection, and persistent memory. Homeostasis is defined as robust viability within a controlled invariant set. Pathophysiology is derived from failures of viability, reserve, transport, energetic payment, repair, and tissue topology. Aging is represented as cumulative repair debt under finite optimally allocated maintenance power, declining physiological integration, increasing frailty, and eventual loss of the energetically constrained viability kernel. The resulting twelve-chapter architecture provides a noncircular mathematical framework for deriving multicellular physiology and its failure modes without introducing additional biological substances or independent physical axioms. **Keywords** Global realism; axiomatization of biology; physiology; homeostasis; multicellular regulation; topological biology; disturbance-field memory; neural signaling; endocrine regulation; muscle contraction; cardiovascular transport; immune recognition; pathophysiology; aging; viability theory.