Correction of an error in my paper ``Continuum equations of balance in classical statistical mechanics''
type: Item
instance of: scholarly article
title: Correction of an error in my paper ``Continuum equations of balance in classical statistical mechanics''
zbMATH Open document ID: 0635.73002
DOI: 10.1007/BF00251520
author: Mario Pitteri
published in: Archive for Rational Mechanics and Analysis
publication date: 1988-01-01T00:00:00Z
review text: [Concerns the author's article, ibid. 94, 291-305 (1986; Zbl 0623.73003).] In addition to a few misprints, I must correct the definition of the function \(\tilde{\mathbf F}_{ij}(x,t)\) at the end of {\S} 2. This definition was intended toproduce integrands \(g(x,y)\) in (3.23) and (3.35) that satisfy the hypotheses of Noll's theorem, in particular condition (3.8). Unfortunately the definition does not serve the purpose for which it was introduced. The conclusions in {\S} 5 remain correct for general forces, but should be changed as follows when \({\mathbf F}_{ij}\), the force that \(P_ j\) exerts on \(P_ i\), is a pairwise interaction which satisfies the Principle of Action and Reaction: in this case internal forces do not contribute to the body force b because \({\mathbf F}_{ij}+{\mathbf F}_{ji}\equiv 0\). As I stated in the paper, non-conservative internal forces do contribute to the heat supply r, even if they are pairwise interactions which satisfy the Principle of Action and Reaction, while inertial frames are indistinguishable. In this case the contribution of those internal forces to r is \[ \sum^{n}_{i\neq j=1}<\phi_{ij}(r_{ij},\| v_ j-v_ i\|,\quad (v_ j-v_ i)\cdot n_{ij})n_{ij}\cdot (v_ i-v_ j)W| x_ i=x>. \]
Mathematics Subject Classification ID: 74Axx
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 4035253
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4035253