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Zeitschrift für Naturforschung A

The Thermal Content of Quantum States

James G. Gilson

Published Feb 1, 1969• 3 citations
Publisher

Abstract

Abstract It is shown that the exact structure of Schrödinger Quantum Mechanics is a consequence of the assumption that there exist two subquantum fluids in local thermal equilibrium.
DOI
10.1515/zna-1969-0203

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The crucial role of counterfactual reasoning in generating inconsistencies between local subquantum theories and quantum mechanics is stressed. It is argued that the physical justification of such reasoning requires the fulfilment of a criterion of actualizability of hypothetical situations. It is demonstrated that in a subquantum framework this criterion is equivalent to the assumption of actual reproducibility of individual subquantum states. Therefore, inconsistencies between local subquantum theories and quantum mechanics disappear if a nonreproducibility property of nature, in full agreement with the empirical fact that past, present and future are basically distinct, is invoked. The proposal also leaves the universal validity of the locality principle untouched, in agreement with all existing empirical evidence.
Abstract Equilibrium statistical mechanics rests on the assumption of chaotic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs’ ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant conservation laws in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics of Floquet systems has a much richer structure due to the existence of emergent conservation laws: these are approximate but stable conservation laws arising due to the drive, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This indicates to the possibility of stable Floquet phases of matter in disorder-free systems. This review intends to give a self-contained theoretical overview of these developments for a broad physics audience. We conclude by briefly surveying the current experimental scenario.
We discuss two-dimensional Madelung fluid dynamics whose irrotational case reduces into the Schrödinger equation for a free single particle. We show that the self-trapped spinning-stationary Madelung fluid reported in the previous paper can be analogically identified as an equilibrium thermodynamics system. This is done by making correspondence between Shannon entropy over Madelung density and internal energy to be defined in the main text, respectively with thermal-entropy and thermal-internal energy of equilibrium thermodynamics system. This leads us to identify a Madelung fluid analog of thermal-temperature at the vanishing value of which the stationary Madelung fluid will be no more spinning and is equal to the quantum mechanical ground state of a particle trapped inside a cylindrical tube external potential.