Reduction of a mesoscopic level to a level with fewer details is made by the time evolution during which the entropy increases. An extension of a mesoscopic level is a construction of a level with more details. In particular, we discuss extensions in which extra state variables are found in the vector fields appearing on the level that we want to extend. Reductions, extensions, and compatibility relations among them are formulated first in an abstract setting and then illustrated in specific mesoscopic theories.

Department of Mathematics FNSPE Czech Technical University Prague Trojanova 13 Prague 2 120 00 Czech Republic and New Technologies Research Centre University of West Bohemia Univerzitní 8 306 14 Pilsen Czech Republic

École Polytechnique de Montréal C P 6079 succ Centre ville Montréal H3C 3A7 Québec Canada

École Polytechnique de Montréal C P 6079 succ Centre ville Montréal H3C 3A7 Québec Canada; Mathematical Institute Faculty of Mathematics and Physics Charles University Prague Sokolovská 83 186 75 Prague Czech Republic; and New Technologies Research Centre University of West Bohemia Univerzitní 8 306 14 Pilsen Czech Republic

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