Power-series expansion of the Boltzmann equation and reciprocal relations for nonlinear irreversible phenomena

Abstract

The Boltzmann equation subject to a general boundary condition is expanded in a power series with respect to a thermodynamic force disturbing a gaseous system. Recurrence relations between the terms of the expansion are obtained using the main properties of the collision integral and of the gas-surface interaction kernel. The reciprocal relation for nonlinear irreversible phenomena, i.e., a relation between the terms of different orders, is obtained. The relations can be used to estimate the range of applicability of linearized solutions and to predict nonlinear phenomena in gaseous systems.