From the point of view of Schr\”odingerism, a wavefunction-only philosophy,
thermodynamics must be recast in terms of an ensemble of wavefunctions, rather
than classical particle configurations or Copenhagenist “found” values.
Recapitulating the historical sequence, we consider here several models of
magnets that classically can exhibit a phase transition to a low-temperature
magnetized state. We formulate wavefunction analogues including a
“Schr\”odingerist QUantum Ising Model” (SQUIM), a “Schr\”odingerist Curie-Weiss
Model” (SCWM), and others. We show that the SQUIM with free boundary conditions
and distinguishable “spins” has no finite-temperature phase transition, which
we attribute to entropy swamping energy. The SCWM likewise, even assuming
exchange symmetry in the wavefunction. But a variant model with “wavefunction
energy” (introduced in prior communications about Schr\”odingerism and the
Measurement Problem) does have a phase transition to a magnetised state. Our
principle technique involves transforming the problem to one in probability
theory, then applying results from Large Deviations, particularly the
G\”artner-Ellis Theorem. Finally, we discuss Gibbs vs. Boltzmann/Einstein
entropy in the choice of the quantum thermodynamic ensemble, as well as open
problems.
PhySH: quantum theory, quantum statistical mechanics, large deviation & rare
event statistics.
