The conceptual gambit of this article is to propose that the notion of anti-entropy should be complemented by that of exergy investment or destruction, a term first proposed by Zoran Rant in 1956. It argues that one of Bernard Stiegler's most important interventions into deconstruction is the thermodynamic reformulation of Derridean "différance." I argue that we should view the idea of anti-entropy as likewise the displacement of entropy to an external system. With the notion of exergy, it becomes possible to outline an economics of exergy expenditure and investment that considers this displacement. Having argued for the necessity of exergy as a concept that may complement anti-entropy, I demonstrate that this economy of exergy expenditure, through transductive analogy, can be applied to signification. An economics of exergy may give crucial insight into the transcendental problem of signification; that which Derrida's notion of "différance" first responded to. I ask the question: can a trace-like logic of sense be understood energetically if trace itself is understood to be materially inscribed into the world? Having explored this question, I then outline how education might be understood as both the means through with traditional significations are energetically maintained as well as the means through which metastable significations can be disrupted. I use the recent banning of anti-capitalist literature in the UK as an example of what I call logomachics, a conflict of significative exergetic investment and disinvestment.