In previous research, the author developed a general abstract framework for the exergy content of a system of finite objects [Grubbstrom RW. Towards a generalized exergy concept. In: van Gool W, Bruggink JJC, editors. Energy and time in the economic and physical sciences. Amsterdam: North-Holland; 1985. p. 41-56]. Each such object is characterised by its initial extensive properties and has an inner energy written as a function of these properties. It was shown that if these objects were allowed to interact, there is a maximum amount of work that can be extracted from the system as a whole, and a general formula for this potential was provided. It was also shown that if one of the objects was allowed to be of infinite magnitude initially, taking on the role as an environment having constant intensive properties, then the formula provided took on the same form as the classical expression for exergy. As a side result, the theoretical considerations demonstrated that the second law of thermodynamics could be interpreted as the inner energy function being a (weakly) convex function of its arguments, when these are chosen as the extensive properties. Since exergy considerations are based on the principle that total entropy is conserved when extracting work, these processes would take an infinite time to complete. In the current paper, instead, a differential-equation approach is introduced to describe the interaction in finite time between given finite objects of a system. Differences in intensive properties between the objects provide a force enabling an exchange of energy and matter. An example of such an interaction is heat conduction. The resulting considerations explain how the power extracted from the system will be limited by the processes being required to perform within finite-time constraints. Applying finite-time processes, in which entropy necessarily is generated, leads to formulating a theory for a maximal power output from the system. It is shown that such a theory is possible to develop, and the resulting equilibrium conditions are compared with to those of the exergetic equilibrium. (c) 2007 Elsevier Ltd. All rights reserved.