Reciprocal relations based on the non-stationary Boltzmann equation

The reciprocal relations for open gaseous systems are obtained on the basis of main properties of the non-stationary Boltzmann equation and gas-surface interaction law. It is shown that the main principles to derive the kinetic coefficients satisfying the reciprocal relations remain the same as those used for time-independent gaseous systems [F. Sharipov, Onsager-Casimir reciprocal relations based on the Boltzmann equation and gas-surface interaction law single gas, Phys. Rev. 73 (2006) 026110]. First, the kinetic coefficients are obtained from the entropy production expression; then it is proved that the coefficient matrix calculated for time reversed source functions is symmetric. The proof is based on the reversibility of the gas-gas and gas-surface interactions. Three examples of applications of the present theory are given. None of these examples can be treated in the frame of the classical Onsager-Casimir reciprocal relations, which are valid only in a particular case, when the kinetic coefficients are odd or even with respect to the time reversion. The approach is generalized for gaseous mixtures.