Quantum adiabatic system has a slowly varying hamiltonian respect to time. The dynamics of the wavefunction is automatically slow. It is interesting if we can speed up that process without leaving any distrubances in initial and final wavefunction.
Entropy is not a state variable, and there is a physical difference between it and internal energy.
In the textbook, the ideal gas entropy: S = n * Cv * In (T) +nR * In (V);
There are two problems:
1. The natural logarithm In(x) will submerge the unit system of volume and temperature [m3], [K].
2. The unit of temperature may be [K], or [mK]; the unit of volume may be [m3], or [cm3]. The results are different and the calculation lacks stability.
Entropy is only a process quantity: DS = n * Cv * In (T2/T1) + nR * In (V2/V1); it has physical significance.
Internal energy is a state quantity, and entropy is only a process quantity. There are physical differences between them.
Internal energy U is conserved and can have the meaning of total differential dU = Ut * dT + Uv * dV - correct.
Entropy is only a process quantity, not a state quantity. Total differential is meaningless: dS = St * dT + Sv * dV - - incorrect.
Entropy is not conservative, even in reversible cycles, it can increase or decrease.
Thermodynamics has some problems in describing ideal gases.
1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.
2. New thermodynamics pursues universality, two theoretical cornerstones:
2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.
2.2. Hydrostatic equilibrium: applicable to gases and liquids.
3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.
3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.
4. See Appendix Pictures and Documents for details.