If time-evolution equations are formulated in terms of thermodynamic building blocks, two possibilities arise to judge the consistency of models: By the properties of the building blocks (strong or structural consistency), or solely by the implied evolution equations (weak or dynamic consistency). We propose a straightforward procedure to check for strong consistency by means of the eigenvalues and eigenmodes of the linearized equations, which is related to establishing a fluctuation-dissipation theorem. By applying the general ideas to hydrodynamics, we clarify the role of the controversial diffusion terms in hydrodynamic equations.

• Received 27 April 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.130602