
05383221
j
2009a.00478
Bringuier, E.
From mechanical motion to Brownian motion, thermodynamics and particle transport theory.
Eur. J. Phys. 29, No. 6, 12431262 (2008).
2008
IOP Publishing, Bristol
EN
M65
link between the mechanical and statistical treatments of particle motion in a medium
doi:10.1088/01430807/29/6/013
Summary: The motion of a particle in a medium is dealt with either as a problem of mechanics or as a transport process in nonequilibrium 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 wellstudied 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 timeindependent and timedependent 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 graduatelevel concepts.