Statistical Mechanics, Molecular Modeling, and the Notion of Stress

This hard bound spinoff from a special issue of the “Journal of Elasticity” (volume 100: 1-2) features an English translation of an important 1955 paper by Walter Noll, “Die Herteitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik.” In this paper, Noll addresses and analyses the seminal paper of Irving and Kirkwood, published five years earlier, on “The Statistical Mechanical Theory of Transport Processes. IV, The Equations of Hydrodynamics.” Noll gives new interpretations and provides a firm setting for ideas advanced by Irving & Kirkwood that clearly and directly relate to the basic principles of continuum mechanics. However, the original German paper of Noll seems not to have gained the attention that it deserved as the field of statistical mechanics grew both fundamentally and in applications. By providing an English translation of Noll’s paper, Lehoucq & Von Lilienfeld-Toal have provided a great service to the scientific community. The Noll translation is presented here to expose fundamental ideas of statistical mechanics that are of major importance in the modeling of small-scale behavior and its link to macroscopic observations. In recent years there has been a rapidly increasing reliance upon and interest in multi scale methods in computation. This has accentuated the need to establish meaningful connections between atomistic and continuum descriptions of contact interactions such as stress and heat flux. In recognition of Noll’s contribution, the translation is accompanied by four relevant and invited papers, including one, entitled “Thoughts on the Concept of Stress,” by Noll himself.