Nonminimally Coupled Boltzmann Equation I: Foundations

A note on the comments of arXiv:2003.10154 [gr-qc] to our paper Nonminimally Coupled Boltzmann Equation I: Foundations (arXiv:2002.08184 [gr-qc])

In this note we comment on remarks about our recent effort to understand the specificities of the Boltzmann equation in the context of the alternative theories of gravity with non-minimal coupling between curvature and matter.

Jeans Instability in Non-Minimal Matter-Curvature Coupling Gravity

The weak field limit of the nonminimally coupled Boltzmann equation is studied, and relations between the invariant Bardeen scalar potentials are derived. The Jean's criterion for instabilities is found through the modified dispersion relation. Special cases are scrutinised and considerations on the model parameters are discussed for Bok globules.

Boltzmann's $H$-theorem, entropy and the strength of gravity in theories with a nonminimal coupling between matter and geometry

In this paper we demonstrate that Boltzmann's $H$-theorem does not necessarily hold in the context of theories of gravity with nonminimally coupled matter fields. We find sufficient conditions for the violation of Boltzmann's $H$-theorem and derive an expression for the evolution of Boltzmann's $H$ in terms of the nonminimal coupling function, valid in the case of a collisionless gas in a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker universe. We highlight the implications of this result for the evolution of the entropy of the matter fields, briefly discussing the role played b…

On the Statistical Foundations of Kaluza's Magnetohydrodynamics

The introduction of electromagnetic fields into the Boltzmann equation following a 5D general relativistic approach is considered in order to establish the transport equations for dilute charged fluids in the presence of a weak electromagnetic field. The conserved 5D stress-energy tensor is evaluated using the Jüttner function for non-degenerate relativistic gases in local equilibrium, and the evolution equations for the local thermodynamic variables are established by means of relativistic kinetic theory. An outline of the possibilities offered by the Kaluza-type approach to MHD is also inclu…

统计力学和早期宇宙的描述I.：略非广延宇宙学的基础

Statistical mechanics and the description of the early universe I.: Foundations for a slightly non-extensive cosmology

我们分析了宇宙的热历史是如何受到统计描述的影响，假设偏离通常的玻色-爱因斯坦，费米-狄拉克和玻尔兹曼-吉布斯分布函数。这些偏差代表了与长程力、记忆效应或分形或多重分形空间中的演化有关的非广延效应的可能出现。在早期宇宙中，通常假设分布函数是标准分布函数。然后，考虑在一个更大的理论框架的演变将允许测试这一假设，并将限制其有效性的范围。得到的修正将随温度而变化，因此，非延伸率的可能量的界限也将随时间而变化。我们推广的结果，可以在其他情况下使用，以及玻尔兹曼方程和萨哈定律，并提供了一个估计如何已知的宇宙学界的中微子的质量修改的变化的统计。我们在这里特别分析了复合时期，明确使用所涉及的化学势，以获得必要的修正。所有这些结果构成的基本工具，需要放置在不同的时代，可能存在的非扩展性的量的界限，并将在以后用于研究原始核合成。

相对论带电气体的动力学理论：流体动力学极限的数学基础及投影方法中的一阶结果

Kinetic theory for a relativistic charged gas: mathematical foundations of the hydrodynamic limit and first-order results within the projection method

通过投影方法对玻尔兹曼方程进行Chapman-Enskog展开，推导相对论带电气体的一阶本构方程，并证明迹固定粒子帧是构建耗散相对论流体理论的自然选择。