Quantum Mechanics and Thermodynamic Continuity. II

Alfred Landé

Partha Ghose, Manoj K. Samal

Alfred Landé

The program of deducing quantum mechanics from the postulate of thermodynamic continuity is extended to embrace the principles of symmetry and quantum statistics, in particular the rule of conservation of symmetry type when a system of N particles in resonance interaction is augmented by one more particle. The special quantitative definition of quantum conjugacy contained in the commutation rule of Born and in the Schrödinger replacement of the momentum p by a differential operator may be replaced by a general qualitative physical definition: “p and q are conjugate observables in a mechanical system when the manifold of q reactions of the system uniquely determines the manifold of its p reactions.” When interpreted in terms of superposition mechanics this definition leads to the rules of Born and Schrödinger and from there to quantum dynamics.

Yu. G. Rudoy, Enock Oluwole Oladimeji

In this paper the detailed investigation of one of the most interesting models in the non relativistic quantum mechanics of one massive particle i.e., introduced by G. Poeschl and E. Teller in 1933 is continued; the starting point of dynamic analysis for potentials, wave functions and energy spectrum was carried on by the same authors in the paper. The generalization of these results on the case of nonzero temperature includes the approximate calculation of the partition function of the model and then also the Massieu Planck thermodynamic potential and its most important derivatives, i.e. internal energy, heat capacity and pressure. The analysis of the results is carried on separately for low and high temperature regions because of the lack of exact unifying expressions of the potential at all temperatures.

Alfred Landé

Ronnie Kosloff

Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law, I-law, II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistency between the two theories, which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis, pointing to flaws in approximations.