Fluctuation theory of media with pronounced spacetime inhomogeneity

A nonlinear determinstic thermodynamics is constructed for media with pronounced (r,t) inhomogeneity of the intensive variables or their derivatives. The balance equations in the theory are taken to be either the equations of an ideal fluid or an ideal fluid with heat conduction. The basic variables are taken to be (r,t) andT(r,t). The hypothesis of local equilibrium is represented in the form of the Gibbs-Duhem relation, the conjugate coordinates are (r,t) and (r,t), and the local potential isP(,T). The velocity potentialv _i (r,t) enters through the substantial derivative. A variational principle is formulated; in the case of an ideal fluid with heat conduction there arises naturally a local decrease of the entropy production:z ₂(t)=z ₀ ² exp(–2t/t), there0074 is the relaxation time.In memory of D. N. ZubarevJoint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 53–67, October, 1993.