  This note reviews the studies of the last decades emphasizing a common
principle based on entropy, logarithmic Sobolev inequality and
hypercontractivity, behind four most celebrated inequalities by M. Talagrand:
the convex distance inequality, the $\mathrm {L}^1$-$\mathrm {L}^2$ variance
inequality, the quadratic transportation cost inequality, and the inequality on
the supremum of empirical processes.
