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We study the quantum to classical transition in a chaotic system surroundedby a diffusive environment. The emergence of classicality is monitored by theRenyi entropy, a measure of the entanglement of a system with its environment.We show that the Renyi entropy has a transition from quantum to classicalbehavior that scales with $\hbar^2_{\rm eff}/D$, where $\hbar_{\rm eff}$ is theeffective Planck constant and $D$ is the strength of the noise. However, it wasrecently shown that a different scaling law controls the quantum to classicaltransition when it is measured comparing the corresponding phase spacedistributions. We discuss here the meaning of both scalings in the precisedefinition of a frontier between the classical and quantum behavior. We alsoshow that there are quantum coherences that the Renyi entropy is unable todetect which questions its use in the studies of decoherence.

Scaling laws in the quantum to classical transition in chaotic systems