Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance

The possibility is examined to give rigorous expressions for kinetic coefficients such as heat conductivity, diffusion constant, thermoelectric power and so on which relate the flow of a certain kind to the generalized forces of thermal nature. We take here as the fundamental assumption Onsager's assumption that the average regression of spontaneous fluctuation of macroscopic variables follows the macroscopic physical laws. The kinetic coefficient G j l appearing in the phenomenological equation, \(\dot{\alpha}_{j}{=}\sum G_{jl}(\partial S/\partial\alpha_{l})\) is shown then to be expressed as \begin{aligned} G_{jl}{=}(k\beta)^{-1}{\int}_{0}^{\infty}d\tau{\int}_{0}^{\beta}<\dot{\alpha}_{l}(-i\hbar\lambda)\dot{\alpha}_{j}(\tau)>d\lambda \end{aligned} where k is the Boltzmann constant and β=1/ k T . This is the same type of formula as we have for kinetic coefficients for mechanical disturbances (Kubo, J. Phys. Soc. 12 (1957) 570). The theory is illustrated for the example of electronic transport phenomena.