Extended irreversible thermodynamics

Over the last decades, many efforts have been displayed to generalize the classical laws of Fourier (heat conduction), Fick (matter diffusion), Newton (viscous flows) and Ohm (electrical transport). Indeed, modern technology strives towards miniaturized devices, high frequency and strongly non-linear processes requiring for a new conceptual approach. Several classes of theories have been developed with this objective and one of them, known under the heading of Extended Irreversible Thermodynamics (EIT) has raised a particular growing interest. The paternity of EIT can be traced back to James Clerk Maxwell who in 1867^{[citation needed]} introduced time derivative terms in the constitutive equations of ideal gases.

The basic idea underlying EIT is to upgrade to the status of independent variables the non-equilibrium internal energy, matter, momentum and electrical fluxes. The choice of the fluxes as variables finds its roots in Grad's thirteen-moment kinetic theory of gases, which therefore provides the natural basis for the development of EIT. The main consequence of the selection of fluxes as state variables is that the constitutive equations of Fourier, Fick, Newton and Ohm are replaced by first-order time evolution equations including memory and non-local effects. The selection of the fluxes as variables is not a mere arbitrary act if it is recalled that in the everyday life, fluxes may play a leading role^{[citation needed]} as for instance in traffic control (flux of cars), economy (flux of money), and the World Wide Web (flux of information).