Nonequilibrium Displacement Variables of Mayer and Co-workers

In 1965, Joseph E. Mayer (Sidebar 13.5) and co-workers published a paper [M. Baur, J. R. Jordan, P. C. Jordan, and J. E. Mayer. Towards a Theory of Linear Nonequilibrium Statistical Mechanics. Ann. Phys. (NY) 65, 96-163 (1965)] in which the vectorial character of the thermodynamic formalism was suggested from a statistical mechanical origin. Although this paper attracted little attention at the time, its results suggest how thermodynamic geometry might be traced to the statistics of quantum mechanical phase-space distributions. 

Mayer et al. begin with the fundamental equation in the Boltzmann-reduced entropy representation 

Because S is a linear operator and WQq is a non-negative function, the expression on the right can be shown to have all the necessary properties of a scalar product, provided that Weq and the phase-space functions F, G appropriate to each thermodynamic variable can be defined and the integral exists. Equation (13.53) is then treated as the equilibrium dot product inherited from the phase-space vectors and dot product in (13.54). 

The couple s move to the University of Chicago (1946-1960) somewhat improved Maria s academic appointment [to voluntary Associate Professor of Physics at Chicago 

In 1960, the Mayers moved to the University of California at San Diego, where both could finally hold full professorships, his in chemistry and hers in physics. But shortly after arrival, Maria suffered a stroke and was troubled thereafter by poor health, succumbing finally (after a prolonged coma) in 1972. While continuing collaborative theoretical chemistry studies, Joseph Mayer helped to build the newly formed UCSD chemistry faculty to national prominence. He retired and remarried, then accepted a term of presidency of the American Physical Society (1973) and continued other professional activities until his death in 1983. 

---