Reciprocal symmetry f_s(z)=f_s(1/z) implies local constraints on multiplicity distributions at n=<n> that hold to leading order in ATLAS data, plus a model-independent entanglement entropy expression S=ln<n>+1-½∫e^{-z}f_s²(z)dz+O(f_s³).
Quantum information approach to high energy interactions
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An approximate formula for the entropy of the negative binomial distribution is provided, with up to ~20% deviation from exact values for extreme parameters.
Including soft gluons in Monte Carlo generators for DIS aligns parton distributions with inclusive PDFs and makes entropy grow with decreasing x, indicating initial-state origin of the bulk entropy.