On Schrödingerist Quantum Thermodynamics

Abstract

From the point of view of Schrödingerism, 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 "Schrödingerist QUantum Ising Model" (SQUIM), a "Schrödingerist 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 Schrödingerism 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 Gärtner-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

A correction related to the ellipse figure, some conceptual comments and improvements in the proof of Theorem Two are added with respect to previous versions. In the journal version, first line after (15) page 5: "...and the O_i's are self-adjoint operators diagonal in the same base as H_{QM}" should be "...and the O_i's are self-adjoint operators such that (sum_i O_i)^2 is self-adjoint too"