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For a thermally elastic network, estimate one elastically active element per mesh volume. Each contributes an elastic free-energy scale of order $k_{B}T$, giving the entropic network modulusat $T=298\mathrm{K}$. Mesh size alone would not determine the modulus of an arbitrary bending-dominated or athermal network; this is the entropic scaling assumption needed for the estimate.

The formal elastic intercept in the given model is consequentlyThe corresponding three-dimensional root-mean-square displacement is about $0.20\mu \mathrm{m}$. The temperature cancels from this estimate because the assumed modulus is itself proportional to $T$. This is the extrapolated plateau from the preceding part, not a nonzero exact zero-lag displacement. Here $m/a=1/2$, so a continuum estimate is only approximate.

In passive microrheology, track dilute inert probe spheres by video microscopy and average squared lag displacements over starting times and probes. An isotropic two-dimensional image gives $⟨\Delta r^2{⟩}_{3d}=(3/2)⟨\Delta r^2{⟩}_{2d}$. Alternatively, dynamic light scattering probes ensemble displacement statistics; the original optical microrheology study compared inferred storage and loss moduli with mechanical measurements.^[ref]

Remove drift, calibrate spatial scale and frame timing, estimate localization noise using an immobilized-bead control, and account for motion blur. Keep probes away from walls and check that changing probe radius or tracer concentration does not change the inferred bulk response unexpectedly. Noise alone can generate a false short-time intercept, while adsorption or confinement can mimic elasticity. No numerical long-time slope is fixed because a numerical viscosity is not supplied.