2011/01/15 by R. E. Lagos, Roberto E. Lagos, Tania P. Simões · 20 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann equation #Brownian motion #Charged particle #Classical mechanics #Entropy (arrow of time) #Non-equilibrium thermodynamics #Physics #Quantum mechanics #Smoluchowski coagulation equation #Statistical Mechanics and Entropy #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.physa.2010.12.032
published in Physica A Statistical Mechanics and its Applications 390(9), 1591-1601 (Elsevier BV) · Minor corrections in this version. Published in Physica A 390, 1591 (2011)
openalex publication_date 2011/01/15 · arxiv created 2013/07/31 · arxiv updated 2013/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.