Abstract In this paper, we analyze the consequences of mass and energy conservation and the second law of thermodynamics for economic activity. In contrast to former studies, we deduce our results formally from a general model of production and consumption. We show that in a static setting for economies containing irreversible processes, a non-zero resource input as well as non-zero emissions are necessary to sustain a positive level of consumption. We generalize this result to a dynamic setting and apply it to the growth discussion and the sustainability discourse. Thereby we show that limits to growth of production and consumption are likely to exist and that the concept of weak sustainability is either morally unattractive or physically infeasible.