A nonlocal heal conduction model, based on nonequilibrium thermodynamics, is proposed. This is achieved by introducing a supplementary stale variable, besides the internal energy. Compatibility with the second law of thermodynamics is examined. The analysis is limited to a linear and weakly nonlocal description.
Lebon, G., & Grmela, M. (1996). Weakly nonlocal heat conduction in rigid solids. Physics Letters. Section A: General, Atomic and Solid State Physics, 214(3-4), 184-188. https://doi.org/10.1016/0375-9601(96)00159-4 (Original work published 1996)