  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 "found" values of Copenaghen Quantum
Mechanics. 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 (in this case the
analytical argument is not totally satisfactory and we helped ourself with a
computer analysis). 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. The three results together
suggest that magnetization in large wavefunction spin chains appears if and
only if we consider indistinguishable particles and block macroscopic
dispersion (i.e. macroscopic superpositions) by energy conservation. 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.
  https://github.com/leodecarlo/Computing-Large-Deviation-Functionals-of-not-identically-distributed-independent-random-variables
