2.3 Equilibrium and transport properties
According to equilibrium statistical mechanics, in a uniform temperature fluid, the molecular velocities will be Maxwellian, and the energy components related to the various degrees of freedom will satisfy the equipartition principle. Thus, the equilibrium probability density function (PDF) of each of the cartesian components of the particle in the above example Ui, will follow the Maxwell-Boltzmann (MB) distribution. Another important application of the Onsager regression relationship (Eq. 6) is the emergence of a class of relationships that relate transport properties to correlation functions known as the Green-Kubo relationships [13, 17]. These relationships are also a consequence of the fluctuation-dissipation theorem. Thus,
γ =(1/d) ∫ dt 〈A(0) • A(t)〉. (Eq. 10)
Here, γ is the transport coefficient of interest, t is time, d is the dimensionality, A is the current that drives it. The integrand of (Eq. 10) is the autocorrelation function (ACF) of quantity A. One can calculate the transport coefficients such as diffusion D, shear viscosity ηs, and thermal conductivity k using the Green-Kubo formula.