Physical Generalizations of the Renyi Entropy

Understand

We present a new type of generalization of the Renyi entropy that follows naturally from its representation as a thermodynamic quantity.

• We apply it to the case of d-dimensional conformal field theories (CFTs) reduced on a region bounded by a sphere.
• It is known how to compute their Renyi entropy as an integral of the thermal entropy of hyperbolic black holes in (d+1)-dimensional anti-de Sitter spacetime.
• We show how this integral fits into the framework of extended gravitational thermodynamics, and then point out the natural generalization of the Renyi entropy that suggests itself in that light.