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International Journal of Geometric Methods in Modern Physics

The irreversible quantum

Pedro Fernández de Córdoba, J. M. Isidro, Milton H. Perea, Joan Vázquez Molina

Published Oct 7, 2014• 4 citations
Publisher

Abstract

We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear regime of irreversibility considered here corresponds to the semiclassical approximation in quantum mechanics. An important issue we address is how the irreversibility of time evolution in thermodynamics is mapped onto the quantum-mechanical side of the correspondence.

DOI
10.1142/s0219887815500139

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We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear regime of irreversibility considered here corresponds to the semiclassical approximation in quantum mechanics. An important issue we address is how the irreversibility of time evolution in thermodynamics is mapped onto the quantum-mechanical side of the correspondence.
We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear regime of irreversibility considered here corresponds to the semiclassical approximation in quantum mechanics. An important issue we address is how the irreversibility of time evolution in thermodynamics is mapped onto the quantum-mechanical side of the correspondence.
The emergent nature of quantum mechanics is shown to follow from a precise correspondence with the classical theory of irreversible thermodynamics. Specifically, the linear (or Gaussian) regime of the latter can be put in a 1-to-1 map with the semiclassical approximation to quantum mechanics. The very possibility of reinterpreting quantum mechanics as a thermodynamics proves that the former is an emergent phenomenon. That is, quantum mechanics is a coarse-grained description of some underlying degrees of freedom.
The emergent nature of quantum mechanics is shown to follow from a precise correspondence with the classical theory of irreversible thermodynamics. Specifically, the linear (or Gaussian) regime of the latter can be put in a 1-to-1 map with the semiclassical approximation to quantum mechanics. The very possibility of reinterpreting quantum mechanics as a thermodynamics proves that the former is an emergent phenomenon. That is, quantum mechanics is a coarse-grained description of some underlying degrees of freedom.
We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.
Motivated by the conceptual problems concerning the quantisation of gravity, the Dutch theoretical physicist G. 't Hooft (1999 Nobel prize in physics) put forward the notion that quantum mechanics must be the emergent theory of some underlying, deterministic theory.This proposal usually goes by the name quantum mechanics as an emergent phenomenon.This research line, initiated by 't Hooft in the late 1990's, has been the subject of intense research over the last 15 years, by 't Hooft himself as well as by many other researchers.In this PhD thesis we present our own approach to quantum mechanics as an emergent phenomenon.According to the emergence paradigm for quantum mechanics, information-loss effects in the underlying deterministic theory lead to the arrangement of states of the latter into equivalence classes, that one identifies as quantum states of the emergent quantum mechanics.In brief, quantisation is dissipation, according to 't Hooft.Moreover it has been argued in the literature that, in the presence of weak gravitational fields, quantum effects must be indistinguishable from thermal effects.Since the latter are typically dissipative in nature, the presence of a weak gravitational field should provide a framework in which quantum effects can be explained as due to thermal, dissipative fluctuations.Furthermore, since gravitational effects can be locally gauged away (thanks to the equivalence principle), there should exist some kind of equivalence principle for quantum effects, i.e., some kind of relativity principle for the notion of quantumness as opposed to the notion of classicality.In this PhD thesis we elaborate on this idea.Once a reference frame is fixed, however, quantum effects cannot be gauged away, and the statement quantisation is dissipation lends itself to a thermodynamical treatment.In this thesis we also present one mechanism whereby quantum mechanics is seen to emerge, thus explicitly realising 't Hooft's proposal.This mechanism is based on a dictionary between semiclassical quantum mechanics, on the one hand, and the classical theory of irreversible thermodynamics in the linear regime, on the other.This thermodynamical formalism, developed by Nobel prize winners Onsager and Prigogine, can be easily mapped into that of semiclassical quantum mechanics. Chapter 3Emergent QM as a thermal ensemble This chapter is based on the article Emergent Quantum Mechanics as a Thermal Ensemble, by P.
It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool toward this goal, we propose a thermodynamical approach to quantum mechanics, based on Onsager's classical theory of irreversible processes and Prigogine's nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conjugate variable corresponding to the entropy is a dimensionless evolution parameter. Contrary to the Hamiltonian, the entropy operator is not a conserved Noether charge. Our construction succeeds in implementing gravitationally-induced irreversibility in the quantum theory.