Charged Brownian Particles: Kramers and Smoluchowski Equations and the Hydrothermodynamical Picture

Abstract

We consider a charged Brownian gas under the influence of external and non uniform electric, magnetic and mechanical fields, immersed in a non uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle's density, a Smoluchowski-reactive like equation; for the particle's momentum density, a generalized Ohm's like equation; and for the particle's energy density, a Maxwell-Cattaneo like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non linear reactive kinetics and a mean field approach to interacting Brownian particles.

Minor corrections in this version. Published in Physica A 390, 1591 (2011)

References in corpus (11)

• Artificial Brownian motors: Controlling transport on the nanoscale
• Heat Transport in low-dimensional systems
• Stochastic thermodynamics of chemical reaction networks
• Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
• Fluctuation relations for a driven Brownian particle
• Entropy production for mechanically or chemically driven biomolecules
• Brownian motion of a charged particle driven internally by correlated noise
• Langevin dynamics in crossed magnetic and electric fields: Hall and diamagnetic fluctuations
• Multiple time-scale approach for a system of Brownian particles in a non-uniform temperature field
• Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state
• Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

Cited by in corpus (5)

• Thermal decay rate of a metastable state with two degrees of freedom: dynamical modeling versus approximate analytical formula
• Thermal decay of a metastable state: the influence of the re-scattering on the quasistationary dynamical rate
• Hot Brownian Carriers in the Langevin Picture: Application to a simple model for the Gunn Effect in GaAs
• Classical and quantum Brownian motion in an electromagnetic field
• Quantum kinetic theory of flux-carrying Brownian particles