We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing Rényi entropies of order $\eta$, of which Shannon entropy is the special case $\eta =1$. The order of Rényi entropy is determined by the way the spectra are sampled. Our derivation also suggests a modification of Rényi entropy, giving it a nontrivial $\eta \to 0$ limit. We show that the sharper peaks generally obtained in ASM are associated with entropies of order $\eta <1$. Our paper provides a generalization of the maximum entropy method that enables extracting more structure than the traditional method.

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• Inverse problems
• Shannon entropy
• Strongly correlated systems
• Monte Carlo methods