Speaker
Description
We develop a statistical framework for logarithmic corrections to black-hole entropy by modeling the horizon as a collection of $N$ identical, non-interacting quantum regions, each carrying a finite set of commuting discrete observables. For fixed collective observables, the horizon is described microcanonically, and a statistical analysis yields
$$
S_{\mathrm{micro}}(A)= \alpha\, \frac{A}{\ell_p^2}-\frac{k}{2}\ln\!\frac{A}{\ell_p^2}+O\!\left(\sqrt{\ell_p^2/A}\right),
$$
where $\alpha$ is a model-dependent constant and $k$ is the number of independent observables per elementary region. This identifies the logarithmic coefficient as a direct measure of the microscopic data used to characterize the horizon states. We then extend the construction to a generalized canonical setting in which $r$ observables fluctuate due to coupling to an external environment, obtaining a unified entropy formula in which the logarithmic term becomes
$$
-\frac{k-r}{2}\ln\!\frac{A}{\ell_p^2}.
$$
As a concrete toy model, each horizon cell is endowed with an $SU(2)\times U(1)\times SU(3)$ structure, leading to
$$
S(A)= \alpha\, \frac{A}{\ell_p^2}-\frac{3}{2}\ln\!\frac{A}{\ell_p^2}+\cdots .
$$
Beyond the black-hole setting, the formalism applies to general composite quantum systems consisting of many identical weakly correlated subsystems described by discrete commuting collective observables, thus predicting a universal logarithmic correction under these general assumptions.