We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequalities for log-concave random variables.

翻译：我们证明，对于具有固定方差的对数凹实随机变量，香农微分熵在指数随机变量下取得最小值。我们应用此结果推导具有对数凹噪声的加性噪声信道容量的上界。我们还改进了对数凹随机变量的反向熵功率不等式中的常数。