2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215277A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are established. This paper is a continuation of the paper of Hiai and Petz in Banach Center Publications, Vol. 78.21 pagesProbabilityStatistics Theory62B10; 94A17text