HoloCyclic Cosmology: A Thermodynamic Derivation of Variable Cosmological Constant in a Closed Cyclic Universe

We present a closed cyclic cosmological model in which the effective cosmological constant Λ(a) is derived from the first law of thermodynamics applied to the cosmologicalhorizon, without invoking scalar fields, modified gravity, or observational fine-tuning. Fora closed (k = +1) universe, the derivation yields Λ(a) = Λ0 − 3/a2. The resulting Friedmann dynamics naturally produce a turnaround point (Tmin) where expansion halts andreverses, followed by collapse toward a singularity (Tmax). The second law of thermodynamics forbids a bounce, as total entropy grows monotonically throughout the cycle.The model resolves the “beginning” problem by closing time cyclically, with entropy resetvia holographic renormalisation in the Planck regime — an open question for quantumgravity. The model makes testable predictions: measurable positive spatial curvature,evolving dark energy equation of state, and possible large-scale CMB anomalies.