The Cost of Becoming: Entropy, History, and Cosmological Closure

This paper develops the Principle of Closure: the claim that a universe containing genuine physical history may require global conditions under which the cumulative cost of irreversible becoming remains physically intelligible as a whole. Modern cosmology successfully describes large-scale evolution, yet physical history presupposes more than succession in time. It requires persistent traces through which prior states remain materially legible in later ones. Such traces depend upon effectively irreversible processes that consume free-energy gradients, generate entropy, and carry cumulative thermodynamic significance. A structural question then arises: if cosmology treats the universe as the total physical system, within what framework is the total cost of irreversible history to be understood? The paper argues deductively that closure is not an optional metaphysical addition, but a consequence of the demand that cumulative becoming be coherent at the scale of the whole. Without some form of closure, irreversible history remains locally describable yet globally unresolved. Situated at the intersection of cosmology, thermodynamics, general relativity, and philosophy of physics, this work proposes a foundational constraint on any theory of a history-bearing universe.