Boltzmann approach to non-linear transport and new thermodynamic forces

We rigorously derive the phenomenological textbook equations for the charge and heat transport starting from the Boltzmann equation in the relaxation time approximation. Our derivation also exposes some limitations of these textbook equations which might become relevant for ever smaller devices. Already to linear order in the driving forces, i.e., the gradients of temperature, electrical and chemical potential, additional terms which have been hitherto neglected appear. These are relevant in the vicinity of an interface. In higher orders, we identify additional thermodynamic forces that contribute to the transport.