This work presents a thermodynamic framework for cosmic acceleration based on a universal persistence condition governing structured systems. Any system that maintains stable correlations must satisfy an inequality between its rate of information accumulation and the thermodynamic cost of erasure. Under a stated modelling assumption (A5) that the cosmological vacuum behaves as an effective correlation-accumulating medium, the monotonic cooling of an expanding universe enables a deferred-erasure mechanism with measurable cosmological consequences. Within this framework, an effective cosmological term is derived as a function of the vacuum’s information accumulation history, yielding a dynamical dark energy density governed by a single scaling parameter. The model produces a closed-form equation of state for dark energy, with distinct regimes that are directly testable with upcoming surveys including DESI and Euclid. It further establishes a correspondence between the observed low-entropy initial condition of the universe and the state that maximizes total deferred-erasure yield, while identifying the arrow of time as the direction of thermodynamically profitable erasure deferral. This is a framework paper: the results are contingent on the stated vacuum information accumulation hypothesis and do not derive it from a microscopic theory. The contribution is a falsifiable, overconstrained cosmological model linking dark energy dynamics, thermodynamic information processing, and coherence-based structure formation.