  One of the challenges in quantum information science is to control open
quantum systems with a large number of qubits. An important aspect of many-body
systems is the emergence of collective phenomena. One collective noise model is
an open atomic system in an electromagnetic environment. This model was
considered by Dicke in the 50's Dicke. In this paper, we study the entropic
decay in Dicke's model and other related collective noise models. Specifically,
we develop a general framework to estimate the spectral gap and modified
logarithmic Sobolev constant of these collective noise models. In addition, we
study the necessary mixing conditions a general Dicke's model must satisfy in
order to have a unique equilibrium state. The combination of representation
theory and entropy estimates could be a guideline to study more general
collective noise models.
