Differential entropy is the extension of Shannon entropy to continuous probability distributions, defined as the negative integral of the probability density function times the logarithm of that density over the sample space; parameters are the continuous probability density function and its support, and it persists as a fundamental quantity in information theory, coding theory for continuous channels, and statistical mechanics. [formal: mathematical | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.60]
Accepted ontology entry
differential-entropy
Differential entropy is the extension of Shannon entropy to continuous probability distributions, defined as the negative integral of the probability density function times the logarithm of that density over the sample space; parameters ar…
Definition
Why it is in scope
A human-made mathematical quantity extending Shannon entropy to continuous probability distributions, persisting as a core concept in information theory, statistics, and machine learning.
Names and aliases
- differential-entropyen · CANONICAL
Relations from this entry
- cmsdard4403ny3vv3nkbt821lDEPENDS_ON →
Differential entropy is defined via the continuous probability density function; remove probability distributions and the integral defining differential entropy ceases to operate, satisfying Law 8 removal test.
- cmsfrqasq00aqqszg1stkbizqINSTANCE_OF →
Differential entropy is the specific instance of Shannon entropy applied to continuous (density-based) distributions rather than discrete ones, nearest kind being entropy itself.
- cmsfrqasq00aqqszg1stkbizqDERIVED_FROM →
Differential entropy is the continuous analog of Shannon (discrete) entropy, replacing summation with integration over a probability density. It was derived from Shannon entropy to handle continuous distributions — entropy came first and gives rise to differential entropy as its continuous extension.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Sep 3, 2026, 3:32 AM UTC
- Content hash
- 17013a17e067b19246ae1a4293a9568ac33275aec6aa5cfb3cf7578703161789