Nonequilibrium thermodynamics of multicomponent fluids

我们根据Miyazaki-Kitahara-Bedeaux论文和书中总结的热力学定律要求的守恒定律和不可逆性，得到了多组分流体的密度和质量通量的一般演化方程。其思想是，在多组分流体中，内能不再是一个保守量，但包括质量通量动能在内的总能量是守恒的。因此，吉布斯关系可以用总能量密度来推广。然后动量密度（质量通量密度）进入吉布斯关系。在此基础上，导出了广义吉布斯关系中密集参数的线性不可逆热力学。进一步，假设演化方程的可逆部分具有辛性质，自动满足无熵产生的条件，我们推导了演化方程的可逆部分，这对于多组分流体的质量通量是不知道的。由于我们的公式是基于熵的概念，我们将玻尔兹曼-爱因斯坦原理推广到多组分流体的无平衡涨落。特别对非平衡反应扩散系统的空间相关性进行了详细的研究，并进行了计算机模拟。最后，在线性流体力学的框架下，从微观的刘维尔形式出发，证明了热力学结果的正确性。

We obtained the general evolution equations for the density and mass flux of each component of a multicomponent fluid on the basis of conservation laws and irreversibility, which are required from the thermodynamic laws, as summarized in the Miyazaki-Kitahara-Bedeaux paper and in the book. The idea is that in a multicomponent fluid, internal energy is no more a conservative quantity, but the total energy including the kinetic energy of mass fluxes is conserved. Thus the Gibbs relation is generalized in terms of total energy density. Then the momentum densities ( mass flux densities) enter into the Gibbs relation. Then we derived linear irreversible thermodynamics in terms of intensive parameters, which appear in the generalized Gibbs relation. Furthermore, assuming the reversible part of the evolution equation has a symplectic property, which automatically satisfies the condition of no entropy production, we derived the reversiblepart of the evolution equation, which was not known for the mass flux of multicomponent fluids. Since our formulation is based on the entorpy concept, we generalized Boltzmann-Einstein principle to none quilibrium fluctuation of multicomponent fluids. Especially, thespatial correlation in nonequilibrium reaction-diffusion systems was studied in detail together with computer simulations. Finally, in the frame of linear hydrodynamics, we proved the thermodynamic results are correct from the microscopic Liouville formalism.