Rényi entropy of order α for a discrete probability distribution P = {p_i} is H_α(P) = (1/(1-α)) · log(Σ_i p_i^α), for α ≥ 0, α ≠ 1. At α = 1 it reduces to Shannon entropy by continuous limit. For α → 0 it gives Hartley entropy; for α → ∞ it gives min-entropy. It serves as a generalized measure of uncertainty that trades sensitivity to rare events (low α) against sensitivity to dominant events (high α). [formal: renyi-entropy | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
renyi-entropy
Rényi entropy of order α for a discrete probability distribution P = {p_i} is H_α(P) = (1/(1-α)) · log(Σ_i p_i^α), for α ≥ 0, α ≠ 1. At α = 1 it reduces to Shannon entropy by continuous limit. For α → 0 it gives Hartley entropy; for α → ∞…
Definition
Why it is in scope
A human-made family of entropy measures parameterized by order α, introduced by Rényi (1961), that generalizes Shannon entropy by trading sensitivity to rare events (low α) against sensitivity to dominant events (high α). Built to persist as a standard tool in information theory, cryptography, and statistical physics.
Names and aliases
- renyi-entropyen · CANONICAL
Relations from this entry
- cmsfxlnqd00qqqszg8hkj1cdgDERIVED_FROM →
Rényi entropy (1961) was introduced as a one-parameter generalization of Shannon entropy (1948). Shannon entropy is the α→1 limit of Rényi's formula. Historical: Shannon existed first and fed into Rényi's generalization.
- cmsfrqasq00aqqszg1stkbizqDERIVED_FROM →
Rényi entropy (1961) was introduced as a one-parameter generalization of Shannon entropy (1948). Shannon entropy is the α→1 limit of the Rényi formula. Historical direction: Shannon existed first and fed into Rényi's generalization.
- cmsdard4403ny3vv3nkbt821lDEPENDS_ON →
Rényi entropy H_α(P) = (1/(1-α)) log Σ p_i^α is defined as a functional of a probability distribution P. Remove the probability distribution and the formula has no inputs; the measure ceases to operate operationally, satisfying Law 8b removal test.
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Record identity
- Created
- Sep 4, 2026, 11:04 AM UTC
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