Abstract The central role of energy in all life processes has lend to the development of numerous hypotheses, conjectures and theories on the relationships between thermodynamics and ecological processes. In this paper we examine the theoretical and empirical support for these developments, and in particular for the widely published set of thermodynamic conjectures developed by H.T. Odum, in which the maximum power principle is put forward as a generic feature of evolution in ecosystems. Although they are widely used, we argue that many of the ecological studies that have adopted the ideas encapsulated in Odum's work have done so without being aware of some of the fundamental problems underlying this approach. We discuss alternative ways in which a general available-work concept could be constructed for use as a numeraire in an energy-centred ecological theory or paradigm. In so doing, we examine what is meant by material accessibility and energy stocks and flows with respect to traditional food webs and food chain theories, and relate these to results from the evolutionary dynamics of ecosystems. We conclude that the various forms and uses of energy bound up in essential ecosystem processes present a formidable obstacle to obtaining an operational definition of a general, aggregated available-work concept, a prerequisite for the systems approach of Odum and others. We also show that the prototypical derivations of the maximum power principle, and its interpretation, are contradicted on many scales both by empirical data and models, thereby invalidating the maximum power principle as a general principle of ecological evolution. The conclusions point to the fundamental problem of trying to describe ecosystems in a framework which has a one-dimensional currency.