A novel approach to a truly dynamic thermodynamics is proposed in which equilibrium is defined in terms of explicit time, distance, and acceptable error scales. This approach involves reformulating the second law of thermodynamics in terms of an excess energy that vanishes at equilibrium instead of an entropy that assumes some unknown maximum value. Excess energy is defined mathematically as the total Legendre transform of energy with respect to an independent set of extensive variables. Excess energy is effectively the free energy functional of a nonequilibrium system and is a function of the time, distance, and acceptable error scales. Elimination of entropy from thermodynamics requires recognizing temperature as a thermal stress, proportional to the antimetric component of the stress tensor that is neglected when one assumes the validity of Cauchy’s second law of motion. The inclusion of temperature as part of the stress-strain couple completes the science of thermomechanics and opens the way for a practical unification of chemistry and physics in strictly mechanical terms.