Statistical Mechanics, Molecular Modeling, and the Notion of Stress: An Invited Collection

Foreword.- Translation of Walter Noll’s “Derivation of the Fundamental Equations of Continuum Thermodynamics from Statistical Mechanics”.- Thoughts on the Concept of Stress.- On Molecular Modelling and Continuum Concepts.- A Unified Interpretation of Stress in Molecular Systems.- On (Andersen–)Parrinello–Rahman Molecular Dynamics, the Related Metadynamics, and the Use of the Cauchy–Born Rule.

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 advancedby 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 behaviour and its link to macroscopic observations. In recent years there has been a rapidly increasing reliance upon and interest in multiscale methods in computation. This has accentuatedthe 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.

English translation of a seminal paper by Noll Of interest to workers in a wide range of currently important fields, including statistical and continuum mechanics and multiscale simulation Additional papers add perspective and depth to the volume