 Entropy power inequality

For independent $n$-dimensional random vectors with densities and finite differential entropies, the entropy power inequality statesThe sum's differential entropy is required to be defined; a value $+\infty$ makes the inequality immediate. Equality for finite nondegenerate densities occurs for Gaussian distributions with proportional covariance matrices.

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The Entropy Power Inequality (EPI) is a fundamental result in information theory that relates the entropy of a sum of independent random variables to their individual entropies.