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Order Structure ( Majorization ) and Irreversible Processes

1. The comparison of the information content of classical or quantum physical states leads to a partial order in the state space of the physical system. This partial order introduced by Uhlmann [68, 69, 71] has (for classical physical systems) well-known roots going back to Schur, Hardy, Littlewood, Polya, Karamata and others. We refer for a survey of these ideas and results (up to 1980) to Thirring [64, 65, 66], Wehrl [89] and the monographs by Alberti & Uhlmann [30, 34, 33].