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Entropy

Entropy in Foundations of Quantum Physics

Marcin Pawłowski

Published Mar 24, 2020• 0 citations
Publisher

Abstract

Entropy can be used in studies on foundations of quantum physics in many different ways, each of them using different properties of this mathematical object [...].
DOI
10.3390/e22030371

Related papers

Entropy in Foundations of Quantum Physics

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This book is a collection of outstanding papers on various aspects of entropy at the foundation of quantum physics. The covered topics range from purely foundational issues such as contextuality and Bell and Leggett–Garg inequalities to applications such as quantum key distribution, teleportation, and image encoding. The main ingredient binding them together in this book is that in all of the contained papers, entropy plays a key role either as a mathematical tool or as a link which bridges the gap between different fields of science.
ABSTRACT. What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental ques-tions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the math-ematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the ther-modynamic equilibrium properties of matter, including entropy values. However, as al-ready recognized by Schrödinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility
Most scholars concerned with the foundations of quantum mechanics (QM) think that contextuality and nonlocality (hence nonobjectivity of physical properties) are unavoidable features of QM which follow from the mathematical apparatus of QM. Moreover these features are usually considered as basic in quantum information processing. Nevertheless they raise still unsolved problems, as the objectification problem in the quantum theory of measurement. The extended semantic realism (ESR) model offers a possible way out from these difficulties by embedding the mathematical formalism of QM into a broader mathematical formalism and reinterpreting quantum probabilities as conditional on detection rather than absolute. The embedding allows to recover the formal apparatus of QM within the ESR model, and the reinterpretation of QM allows to construct a noncontextual hidden variables theory which justifies the assumptions introduced in the ESR model and proves its objectivity. According to the ESR model both linear and nonlinear time evolution occur, depending on the physical environment, as in QM. In addition, the ESR model, though objective, implies modified Bell's inequalities that do not conflict with QM, supplies different mathematical representations of proper and improper mixtures, provides a general framework in which the local interpretations of the GHZ experiment obtained by other authors are recovered and explained, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth.
I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.