Canonical formulation of Thermodynamics, and corresponding wave equation   for far from equilibrium case
  Lagrange and Hamilton equations for thermodynamic evolution near equilibrium as well as Schrodinger-like equation for the non-equilibrium case are obtained extending the CPDQ Principle (Constancy of the product momentum-oordinate uncertainty) to a new conjugate pair where the momentum f is the extension of the mechanical f=p.{\delta}q product for the case the coordinate q is not directly observable. Applied to the case of a particle in a one dimension box, the results are in agreement with reported calculated and measured thermal conductance. 
Adrian Faigon
quant-ph cond-mat.stat-mech