id: 05383221
dt: j
an: 2009a.00478
au: Bringuier, E.
ti: From mechanical motion to Brownian motion, thermodynamics and particle
transport theory.
so: Eur. J. Phys. 29, No. 6, 1243-1262 (2008).
py: 2008
pu: IOP Publishing, Bristol
la: EN
cc: M65
ut: link between the mechanical and statistical treatments of particle motion
in a medium
ci:
li: doi:10.1088/0143-0807/29/6/013
ab: Summary: The motion of a particle in a medium is dealt with either as a
problem of mechanics or as a transport process in non-equilibrium
statistical physics. The two kinds of approach are often unrelated as
they are taught in different textbooks. The aim of this paper is to
highlight the link between the mechanical and statistical treatments of
particle motion in a medium, starting from the well-studied case of
Brownian motion. First, deterministic dynamics is supplemented with
stochastic elements accounting for the thermal agitation of the host
medium: it is the approach of Langevin, which has been rephrased and
extended by Kramers. It handles time-independent and time-dependent
stochastic motions as well. In that approach, the host medium is not
affected by the guest particles and the latter do not interact with
each other. Both limitations are shown to be overcome in
thermodynamics, which however is restricted to equilibrium situations,
i.e. stochastic motions with no net current. When equilibrium is
slightly perturbed, we show how thermodynamic and kinetic concepts
supersede mechanical concepts to describe particle transport. The
description includes multicomponent transport. The discussions of
stochastic dynamics and of thermodynamics are led at the undergraduate
level; the treatment of multicomponent transport introduces
graduate-level concepts.
rv: