Time-Orientation Selection and Matter--Antimatter Asymmetry from Variational Dynamics

This work develops a variational framework in which the arrow of time is treated as a physical, coarse-grained order parameter rather than a fixed boundary condition. After integrating out short-wavelength degrees of freedom, the long-wavelength time orientation obeys deterministic overdamped dynamics governed by an effective potential on a compact configuration space. A small inversion-breaking “tilt” in this potential dynamically selects a unique, linearly stable preferred orientation that minimizes the effective action and defines a global arrow of time. The framework requires no assumption about the microscopic origin of the tilt, which is treated phenomenologically and constrained by observation, and remains compatible with standard effective field-theoretic reasoning . The paper establishes a no-go theorem showing that, in the absence of such a tilt, inversion-symmetric dynamics generically lead either to opposite-orientation domains or to vanishing net matter–antimatter asymmetry unless non-generic initial conditions are imposed. Matter dominance instead emerges as a probabilistic bias determined by the projection of the preferred time orientation onto basin-separating directions in configuration space, yielding an effective asymmetry parameter that maps directly onto standard baryogenesis phenomenology. The results provide a precise conceptual and mathematical link between global arrow-of-time selection and matter–antimatter asymmetry, clarifying why a nonzero symmetry-breaking bias is necessary for a Universe with a coherent time direction and observed matter dominance .