TEMPERATURE AND ENTROPY PRODUCTION OPERATOR IN FOURIER HEAT-CONDUCTION

The Hamilton-Lagrange formalism of the field theory of irreversible no nequilibrium thermodynamics has been developed in the last few years. Consequently, we have a good opportunity to introduce the canonical qu antization for the parabolic differential equations, such as Fourier h eat conduction. This procedure might tell us how quantum features aris e in the system under consideration and how we may get to the quantum field theory of irreversible processes. We introduce the temperature a nd the entropy production operator in the case of the heat equation, a nd we show that the eigenvalues of the entropy production operator are discrete and real quantities.