The reciprocal relations between cross phenomena in boundless gaseous systems

The Onsager–Casimir reciprocal relations obtained for gaseous systems on the basis of the linearized Boltzmann equation in a general form [F. Sharipov, Onsager–Casimir reciprocal relations based on the Boltzmann equation and gas–surface interaction law. Single gas., Phys. Rev. E 73 (2006) 026110] are applied to boundless domains. Under additional assumptions, expressions of the kinetic coefficients obtained previously are significantly simplified and can be easily applied in practice. In contrast to all previous works on this topic, it is shown that for a given set of thermodynamic forces there are several sets of thermodynamic fluxes providing the same entropy production. As a consequence, several forms of the kinetic coefficients satisfying the reciprocal relations do exist for a given set of thermodynamic forces. An illustrative example confirms that in many situations the kinetic coefficients are neither odd nor even with respect to the time-reversal and hence the reciprocal relations between them should be written in more general form than that obtained by Casimir.