2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16724We review the recent result of Sato, Sekimoto, Hondou, and Takagi (cond-mat/0008393) on the irreversibility inevitably observed in systems consisting of many non-interacting ``small'' pieces. We focus on quantum models, and supply an explicit lower bound for the work required to complete a cyclic process.12 pages, 1 figure (The title has been changed to avoid misunderstandings.)Statistical Mechanicstext