It is recognized that orbital forcing of the ice sheet is through the summer air temperature, which however covaries with the sea surface temperature and both precede the ice volume signal, suggesting the ocean as an intermediary of the glacial cycles. To elucidate the ocean role, I present here a minimal box model, which entails two key physics overlooked by most climate models. First, I discern a robust ‘convective’ bound on the ocean cooling in a coupled ocean/atmosphere, and second, because of their inherent turbulence, I posit that the climate is a macroscopic manifestation of a nonequilibrium thermodynamic system. As their deductive outcome, the ocean entails bistable equilibria of maximum entropy production, which would translate to bistable ice states of polar cap and Laurentide ice sheet, enabling large ice-volume signal when subjected to modulated forcing. Since the bistable interval is lowered during Pleistocene cooling, I show that its interplay with the ice–albedo feedback may account for the mid-Pleistocene transition from 41-ky obliquity cycles to 100-ky ice-age cycles paced by eccentricity. Observational tests of the theory and its parsimony in resolving myriad glacial puzzles suggest that the theory has captured the governing physics of the Pleistocene glacial cycles.