On Schr\"odingerist Quantum Thermodynamics

TL;DR

This paper explores how thermodynamics and phase transitions can be understood within a wavefunction-only framework called Schr"odingerism, analyzing models like the quantum Ising and Curie-Weiss models through large deviation theory.

Contribution

It introduces wavefunction-based analogues of classical magnetic models and demonstrates conditions under which phase transitions occur in Schr"odingerist quantum thermodynamics.

Findings

No finite-temperature phase transition in SQUIM with free boundary conditions.

Phase transition observed in a variant with Wavefunction Energy.

Magnetization in wavefunction spin chains depends on indistinguishability and energy conservation.

Abstract

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