This book on energy physics and energy efficiency discusses two essential components of energy physics: the fundamentals and the criteria. It covers the historical basis of Carnot models, the thermostatic cycles of double-function heat pumps and the optimization of thermomechanical engines, and discusses the results of various investigations, bringing together a number of previous works. The latter half of this book introduces the concept of "Circular Thermoeconomics" and assesses the physical costs of recycling waste in increasingly complex industrial processes. It then goes on to present "Relative Free Energy", allowing us to create a new mathematical theory of thermodynamic costs in order to diagnose malfunctions in thermal systems. The book shows the progression of knowledge on the existence of successive energy, power and efficiency, and pairs this with the economic aspects, which are already becoming linked to growing environmental concerns.