Physics · Dynamics
EntropyDensityCollapse#0874
Rescale entropy and density by system size until all samples fall on one curve, then read regimes from the residue
Mechanism
Samples differ in how many agents or interactions fill the same observation area, so raw entropies mix size with structure. Make both quantities intensive: entropy density eta = H / A_o and control parameter rho = N_V / A_o (agent density for an agent network, interaction-event density for an event network). Take the characteristic system size S = <rho> per sample and fit the finite-size scaling ansatz eta(rho, S) = S^alpha f(rho S^-beta): choose alpha and beta (e.g. by Nelder-Mead) to minimise sum_ij (eta_ij S^-alpha - f(rho_ij S^-beta))^2 over samples i and windows j, and bootstrap windows to get exponent uncertainties. A good collapse means a shared scaling law; systematic, regime-labelled departures from the collapsed curve are the signal. Compare the collapse with the same procedure on NullModelBaseline data, and test departures with ClusteredObservationTesting. Interpret exponents too: near-zero exponents with a near-perfect fit mean the measure is simply tracking density.
Invariants
- Entropy and control parameter are both made intensive before fitting
- The same ansatz and optimiser are applied to empirical and null data
- Exponent uncertainties come from resampling, not from a single fit
Failure modes
- Trivial collapse: R^2 near 1 with exponents near 0 because the measure is dominated by density, not structure
- Broad exponent confidence intervals spanning zero signal that no scaling relation is present
- Narrow density range from short laboratory windows leaves the scaling function poorly constrained
- Taking a good collapse as proof of universality when between-sample variance (ICC) is high
Where this came from
- Thesis Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026), Ch. 3.3, Eqs. 3.27-3.28, Fig. 3.6; Ch. 4.2.1; Ch. 5.4
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Identity
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- Sema ID
sema:EntropyDensityCollapse#mh:SHA-256:0874645031ec2852f52b3a5a1c3980055703036ef7278df3aee69c6359559bb3- Reference
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