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1 results

  • 11 - Entropy Modulo a Prime

  • Tom Leinster, University of Edinburgh
  • Book:
    Entropy and Diversity
    Published online:
    21 April 2021
    Print publication:
    22 April 2021, pp 343-367

  • Summary

    Ordinary probabilities are real numbers, and ordinary entropy is a real number too. Building on ideas of Kontsevich, we develop an analogue of entropy in which both the probabilities and entropy itself are integers modulo a prime number p. While the formula for entropy mod p is quite unlike the formula for real entropy, we prove characterization theorems for entropy mod p and information loss mod p that are very closely analogous to the theorems over the real numbers, thus justifying the definition. We also establish a sense in which entropy mod p is the residue mod p of real entropy.