We propose an effective Markovian coarse-grained cosmological framework in which large-scale information dynamics are driven by non-equilibrium fluctuations. Non-equilibrium is quantified by the dimensionless temperature fluctuation intensity phi(t) = (Delta T(t) / T(t))^2. We model dissipation as proportional to this intensity under cosmological coarse-graining. Identifying the effective baseline rate with the Hubble expansion rate H(t), we obtain a cosmological update frequency alpha(t) = H(t) phi(t). The framework combines variational free energy, Fisher information geometry, and an effective Lindblad-type evolution to connect probabilistic mismatch, dissipation, and cosmic expansion. At late times, the model yields a parameter-free prediction alpha_obs = H0 phi_obs, where phi_obs is determined directly from the observed CMB angular power spectrum. This proposal establishes a minimal observationally anchored relation between cosmological expansion and effective information-dynamical evolution within a coarse-grained Markovian description.