Speculation on Two-Level Quantum Carnot Cycle

 In a previous note (1) we argue that the entropy for a pure quantum bound state is given by S=Sx+Sp where Sx = -k{ Integral dx Wn(x)Wn(x)ln(WnWn) + Integral dp an(p)an(p) ln(an an) }.

It was shown that for any energy level pure bound state for the case of a particle in a box with an infinite potential or for an oscillator S does not depend on the parameters L (length of box) or k (spring constant) or m (mass). Thus a quantum adiabatic change of the parameter leaving the particle in the same quantum state leads to no change in entropy.

    In (2) a two level quantum Carnot cycle is considered for a particle in a box with an infinite potential. Energy levels n=0 and n=1 are considered.. The wavefunction is a(1)W1(x) + a(2)W2(x). Shannon’s entropy is used namely  S=-k Sum over n an(an) ln{|an an|} ((1)) and an expression is found linking an*an to L and T (temperature) for a particle in a box with infinite potential walls. A Carnot cycle with two isotherms and two adiabatic dS=0 parts is considered. No consideration is given to the internal entropy of a bound state eigenstate.

   In this note we try to show how the overall entropy changes if the internal bound energy eigenfuntion entropy ((1)) is considered and also show how an*an(T,L) changes. We find that a1*a1 changes as do the overall values of Q (heat) and W(work) for the Carnot cycle, but that the efficiency does not.