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arXiv · 2309.00044

R\'enyi entropies in the $n\to0$ limit and entanglement temperatures

Cesar A. Agón·Horacio Casini·Pedro J. Martinez
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Abstract

Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the $n \to 0$ limit of R\'enyi entropies $S_n$, can be computed from the ET. This establishes a formula for these R\'enyi entropies for any region in terms of solutions of the eikonal equations. In the $n\to 0$ limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.

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Cesar A. Agón, Horacio Casini, Pedro J. Martinez. 2023-08-31. R\'enyi entropies in the $n\to0$ limit and entanglement temperatures. https://arxiv.org/abs/2309.00044

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