a b s t r a c tWe 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 the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle 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.

We report the exact fundamental solution for Kramers equation associated to a brownian gas of charged particles, under the influence of homogeneous (spatially uniform) otherwise arbitrary, external mechanical, electrical and magnetic fields. Some applications are presented, namely the hydrothermodynamical picture for Brownian motion in the long time regime.Comment: minor correction

Specific heat measurements constitute one of the most powerful experimental methods to probe fundamental excitations in solids. After the proposition of Einstein's model, more than one century ago (Annalen der Physik 22, 180 (1907)), several theoretical models have been proposed to describe experimental results. Here we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels ∆i = (Ei − E0) and the degeneracy of each energy level gi, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of ∆2/∆1 ≈ 10 between the energy levels and a high degeneracy of one of the energy levels define the twopeaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.

The magneto-caloric effect (MCE), which is the refrigeration based on the variation of the magnetic entropy, is of great interest in both technological applications and fundamental research. The MCE is quantified by the magnetic Grüneisen parameter Γmag. We report on an analysis of Γmag for the classical Brillouin-like paramagnet, for a modified Brillouin function taking into account a zero-field splitting originated from the spin-orbit (SO) interaction and for the one-dimensional Ising (1DI) model under longitudinal field. For both Brillouin-like model with SO interaction and the longitudinal 1DI model, for T → 0 and vanishing field a sign change of the MCE is observed, suggestive of a quantum phase transition. SO interaction leads to a narrowing of the critical fluctuations upon approaching the critical point. Our findings emphasize the relevance of Γmag for exploring critical points. Also, we show that the Brillouin model with and without SO interaction can be recovered from the 1DI model in the regime of high-temperatures and vanishing coupling constant J.

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The Grüneisen ratio (Γ), i.e. the ratio of the linear thermal expansivity to the specific heat at constant pressure, quantifies the degree of anharmonicity of the potential governing the physical properties of a system. While Γ has been intensively explored in solid state physics, very little is known about its behavior for gases. This is most likely due to the difficulties posed to carry out both thermal expansion and specific heat measurements in gases with high accuracy as a function of pressure and temperature. Furthermore, to the best of our knowledge a comprehensive discussion about the peculiarities of the Grüneisen ratio is still lacking in the literature. Here we report on a detailed and comprehensive overview of the Grüneisen ratio. Particular emphasis is placed on the analysis of Γ for gases. The main findings of this work are: i) for the Van der Waals gas Γ depends only on the co-volume b due to interaction effects, it is smaller than that for the ideal gas (Γ = 2/3) and diverges upon approaching the critical volume; ii) for the Bose-Einstein condensation of an ideal boson gas, assuming the transition as first-order Γ diverges upon approaching a critical volume, similarly to the Van der Waals gas; iii) for 4 He at the superfluid transition Γ shows a singular behavior. Our results reveal that Γ can be used as an appropriate experimental tool to explore pressure-induced critical points.

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