... THE PHYSICS AND MATHEMATICS OF THE SECOND LAW OF THERMODYNAMICS Elliott H LIEB , Jakob YNGVASON Departments of Physics and Mathematics, Princeton University, ... formulations of thermodynamics, including most textbook presentations, suffer from mixing the physics with the mathematics Physics refers to the real world of experiments and results of measurement, the ... pressures and densities), and if we mix them together, then among the states of one mole of nitrogen that can be reached adiabatically there is one in which the energy is the sum of the two energies and, ...