The Casimir effect is the most controlled laboratory interface betweenquantum vacuum fluctuations, geometry and boundary conditions. We arguethat it can also serve as the first experimental gateway intoEntropy-Space: a programme in which forces emerge from informationgradients and from history-dependent entropic response of the vacuum. The Lifshitz formula is adopted as the conservative null model. We first show that the ideal Casimir pressure can be reconstructed froma finite mutual-information functional I (d) = gamma₀ A/d² and amodular energy scale Thetaₘod (d) = hbar c/ (2 pi d), withgamma₀ = pi³/240 spectrally fixed by TE+TM mode counting via thereplica/heat-kernel route. The decisive beyond-Lifshitz signature is dynamical: a multi-cycle loopwork Wₗoop ~ d^ (-5) (sphere-plate Wₗoop ~ R/d⁴ via PFA) with aLorentzian frequency response controlled by an entropic relaxationtime tauS, structurally absent from any conservative single-cycleLifshitz description. The predicted discriminator W (100 nm) /W (300 nm) = 3⁵ = 243 separates the entropic mechanism from mechanical, thermaland electrostatic hysteresis sources. A laboratory measurement of tauS would, via a coarse-graining ratioR = tauₕ/tauS, predict the corresponding macroscopic memory scaletauₕ for a given physical regime. For cluster-merger physics (tauₕ ~ few Myr), R ~ 10²5 links the laboratory and the clusterscale across twenty-five orders of magnitude in time. The full technical apparatus is provided as Supplementary Material atDOI: 10. 5281/zenodo. 14971614.
Pietro Cambi (Mon,) studied this question.