We address the problem of mining maximally informative k-itemsets (miki) in data streams based on joint entropy. We propose PentroS, a highly scalable parallel miki mining algorithm. PentroS renders the mining process of large volumes of incoming data very efficient. It is designed to take into account the continuous aspect of data streams, particularly by reducing the computations of need for updating the miki results after arrival/departure of transactions to/from the sliding window. PentroS has been extensively evaluated using massive real-world data streams. Our experimental results confirm the effectiveness of our proposal which allows excellent throughput with high itemset length.