Information, Entropy, and Constraint

If futures shrink irreversibly, entropy and information must exist. This paper examines how quantitative temporal asymmetry arises once time is established as an ordered structure of irreversible, probabilistically constrained transitions. Building on prior results that derive transition, irreversibility, probability, and temporal order without physical assumptions, it introduces entropy as a minimal, pre-physical measure of irreversible constraint accumulation. Entropy is defined without appeal to thermodynamics, probability distributions, microstates, or observers. Instead, it is shown to emerge as a monotone measure over ordered states, quantifying the strength of temporal asymmetry introduced by irreversible transitions. Information is correspondingly identified as the irreversible resolution of constrained alternatives, linking informational gain to increasing definitiveness rather than to uncertainty or disorder. On this account, entropy does not generate time, but supplies scale and comparative strength to temporal order. The framework establishes entropy as a structural necessity for measurable time, preparing the ground for later examination of how these constraints are realized within physical theories.