Entropy as Constraint Volume: A Unified Structural Origin of Irreversibility

Entropy appears in physics in many forms—thermal, quantum, informational, gravitational—yet its conceptual foundations remain disparate. We propose a unified definition of entropy grounded in global physical constraints. A constraint set C determines the admissible microstate region Γ(C), and the entropy is defined as S(C) = kBlnVolΓ(C). This constraint–volume formulation applies uniformly to classical and quantum systems, to internal and external degrees of freedom, and to finite or continuous state spaces, without invoking coarse-graining, ensembles, or subjective information. Local interactions generically weaken global constraints such as coherence, correlations, gradients, and entanglement structure. We prove a structural Second Law: whenever constraints decay under dynamical evolution, C(t +∆t) ⊆ C(t), the entropy must increase. This mechanism explains thermodynamic irreversibility, decoherence, thermalization, and hydrodynamic mixing as manifestations of constraint erosion, while identifying integrable and symmetry-protected systems as the exceptional cases in which constraints persist. The framework clarifies how macroscopic entropy can grow evenwhenmicroscopic dynamics are reversible, and why time itself is not a form of entropy. Classical thermodynamic entropy, quantum von Neumann entropy, and black hole entropy all emerge as special cases of the same structural principle.