We develop an information-theoretic approach to study the Kneser--Poulsen conjecture in discrete geometry. This leads us to a broad question regarding whether R\'enyi entropies of independent sums decrease when one of the summands is contracted by a $1$-Lipschitz map. We answer this question affirmatively in various cases.

翻译：我们发展了一种信息论方法来研究离散几何中的Kneser-Poulsen猜想。这引出了一个广泛的问题：当其中一个被加项通过1-Lipschitz映射收缩时，独立和的Rényi熵是否减少。我们在多种情况下对该问题给出了肯定回答。