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实值对数凹随机变量，香农微分熵在指数随机变量时取最小值。我们应用此结果推导了对数凹噪声加性噪声信道容量的上界。我们还改进了对数凹随机变量反向熵幂不等式中的常数。