CHAPTER 1 FREE ENERGIES OF STAGING A SCENARIO AND PERPETUAL MOTION MACHINES OF THE THIRD KIND Peter Salamon 1 , Bjarne Andresen 2 , Karl Heinz Hoffmann 3 , James D. Nulton 1 , Anca M. Segall 4 , Forest L. Rohwer 4 1 Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182, USA 2 Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copen- hagen Ø, Denmark 3 Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany 4 Department of Bioology, San Diego State University, San Diego, California 92182, USA 1.1 Abstract It has been stated that certain chains of biological reactions can go to near completion in both directions as needed without any exterior driving force. This claim repre- sents a thermodynamic impossibility. Yet, this impossibility is of a type not usually covered by the traditional list of impossibility devices known as perpetual motion machines. Rather, it represents a perpetual motion machine of the third kind (PM3) that becomes impossible only in finite time. At non-vanishing rate the chain of bio- logical reactions above would constitute a finite-time perpetual motion machine. The resolution of this quandary leads directly to a notion of staging free energy: the free energy invested in choreographing all the actors of a biochemical reaction directing them to the needed places at the needed times. We conclude by noting that biologi- cal systems make ample use of invertible degrees of freedom that often operate near PM3 limits. Please enter \offprintinfo{(Title, Edition)}{(Author)} at the beginning of your document. 1