Time as Constraint Throughput

This paper develops a formal, system-relative notion of time as a derived quantity generated by constrained entropy throughput within Filtration Theory. Time is defined as the accumulation of filtration power under admissible constraints, making explicit a consequence already implicit in the theory’s variational framework. The formulation predicts temporal thinning, desynchronisation, and local saturation of system-relative time without invoking a global background time. Nested systems may therefore generate plural, non-identical temporal structures depending on constraint architecture, environmental coupling, and scale. The results are intended as a formal extension of Filtration Theory (Warwick, 2025) and do not introduce new primitives or modify its core definitions. Testable implications are outlined for biological, cognitive, artificial, and physical systems, with particular relevance to non-equilibrium and adaptive dynamics.