Cite as: doi:10.26081/K6392N

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I will talk about the fluctuation entropy for two-dimensional matter
systems with an internal symmetry coupled to Jackiwâ€“Teitelboim(JT)
gravity joined to a Minkowski region. The fluctuation entropy is the
Shannon entropy associated to probabilities of finding particular charge
for a region. I will first consider a case where the matter has a global
symmetry. The calculation of the fluctuation entropy of Hawking
radiation shows an unbounded growth and exceeds the entanglement entropy
in presence of islands. This indicates that the global symmetry is
violated. I will then discuss the fluctuation entropy for matter coupled
to a two-dimensional gauge field. I will further discuss a lower bound
on the gauge coupling in order to avoid a similar issue. Also, I will
point out a few puzzles related to the island prescription in presence
of a gauge symmetry.
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