Onsager-Casimir principle and the constitutive relations of bi-anisotropic media

In this paper we establish relation between the microscopic and macroscopic Onsager-Casimir principles. It is demonstrated that because of certain symmetries with respect to the space reversal operation, which are intrinsic to any form of the linear constitutive relations, it follows that the symmetries under time reversal expressed by the Onsager-Casimir principle are valid both on the microscopic and macroscopic levels. As one of the possible applications we show that the property of the general bi-anisotropic media to be reciprocal or non-reciprocal does not depend on the constitutive formalism.