Non-equilibrium thermodynamics in multiphase flows
type: Item
instance of: scholarly article
title: Non-equilibrium thermodynamics in multiphase flows
zbMATH Open document ID: 1285.80001
DOI: 10.1007/978-94-007-5461-4
author: Roberto Mauri
published in: Soft and Biological Matter
publication date: 2012-11-15T00:00:00Z
full work available at URL: http://cds.cern.ch/record/1501107
review text: The book is devoted to the description and to the study of non-equilibrium thermodynamics problems occurring in multiphase flows. It is divided into 11 chapters completed with 7 appendices. Each chapter ends with some problems whose solutions are gathered in the last appendix. The first chapter studies the notion of local equilibrium. The author starts with the description of the fluctuations of a thermodynamic quantity around its constant equilibrium value for a system of \(N\) particles at equilibrium and then for an isolated system macroscopically at equilibrium. He then computes the entropy \(S_{tot}\) of the system. In few examples he computes the entropy changes \(\Delta S_{tot}\). Chapter 2 presents the notion of microscopic reversibility. The author introduces the notions of probability distribution and of joint probability and their properties. Then he presents the notion of microscopic reversibility for an \(N\)-body system. Onsager's reciprocity relations are discussed and applied in order to derive a fluctuation-dissipation theorem through the use of Fourier's transform. Chapter 3 starts with the description of Brownian motions in the case of suspended particles, considered as random walks. Langevin's equation is established first in the 1D case and then in a generalized situation. Chapter 4 studies the Fokker-Planck equation. The author starts with a short description of the Markov processes from which he derives the Fokker-Planck equation. The general solution of this equation is given and the chapter ends with some considerations on Wiener processes. Chapter 6 presents some tools of the stochastic differential calculus. As mentioned in the introduction of this chapter, the author here intends to explain this topic ``in a way that is readily understandable also to a non-mathematician''. He presents Ito's and Stratinovich's stochastic calculus applied to the context of equilibrium and fluctuations. Considering a Brownian particle, he describes some noti…
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 80-02
Mathematics Subject Classification ID: 80A17
Mathematics Subject Classification ID: 80M40
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 6107092
zbMATH Keywords: non-equilibrium thermodynamics
zbMATH Keywords: entropy
zbMATH Keywords: reversibility
zbMATH Keywords: Onsager's reciprocity relations
zbMATH Keywords: Brownian motion
zbMATH Keywords: Langevin's equation
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: stochastic differential calculus
zbMATH Keywords: path integral
zbMATH Keywords: balance equation
zbMATH Keywords: constitutive relation
zbMATH Keywords: multicomponent mixture
zbMATH Keywords: multiphase system
zbMATH Keywords: suspension
zbMATH Keywords: porous medium
zbMATH Keywords: effective relation
zbMATH Keywords: homogenization
MaRDI profile type: Publication
OpenAlex ID: W2494052166
description: scientific article; zbMATH DE number 6107092