Simultaneous Brownian Motion of N Particles in a Temperature Gradient
J. M. Rub\'i, P. Mazur
TL;DR
This paper derives a Fokker-Planck equation describing the collective Brownian motion of N particles in a temperature gradient, incorporating hydrodynamic interactions and internal degrees of freedom.
Contribution
It introduces a thermodynamic framework to model N particles' Brownian motion in nonuniform heat baths, including hydrodynamic couplings.
Findings
Derived the Fokker-Planck equation for N particles in a temperature gradient.
Accounted for hydrodynamic interactions between particles.
Provided a thermodynamic approach to non-equilibrium systems.
Abstract
A system of N Brownian particles suspended in a nonuniform heat bath is treated as a thermodynamic system whith internal degrees of freedom, in this case their velocities and coordinates. Applying the scheme of non-equilibrium thermodynamics, one then easily obtains the Fokker-Planck equation for simultaneous Brownian motion of N particles in a temperature gradient. This equation accounts for couplings in the motion as a result of hydrodynamic interactions between particles.
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