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Does the Non-Locality of Quantum Phenomena Guarantee the Emergence of Entropy?

Jonathan J. Dickau

Published Sep 1, 2009• 1 citation
OpenAlex

Abstract

Abstract: Quantum-Mechanical objects and phenomena have a different nature, and follow a different set of rules, from their classical counterparts. Two interesting aspects are the superposition of states and the non-locality of objects and phenomena. A third aspect, that gives quantum-mechanical objects which have common roots a non-local connection, is quantum entanglement. This paper takes up the question of whether these three properties of quantum mechanical systems facilitate the action of entropy’s increase, in terms of creating a condition where energy is dispersing, or going from being localized to being more spread out over time. Quantum Mechanics gives each quantum entity the nature of a container or vehicle for both energy and information, some part of which is necessarily non-local. The author feels that quantum-mechanical systems take on aspects of computing engines, in this context. He discusses how the onset of chaos is possible with even the simplest calculational processes, how these processes also result in complexity building, and why both of these dynamics contribute to the character of entropy as observed in ordinary affairs, or with macroscopic systems.

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Abstract: Quantum-Mechanical objects and phenomena have a different nature, and follow a different set of rules, from their classical counterparts. Two interesting aspects are the superposition of states and the non-locality of objects and phenomena. A third aspect, that gives quantum-mechanical objects which have common roots a non-local connection, is quantum entanglement. This paper takes up the question of whether these three properties of quantum mechanical systems facilitate the action of entropy’s increase, in terms of creating a condition where energy is dispersing, or going from being localized to being more spread out over time. Quantum Mechanics gives each quantum entity the nature of a container or vehicle for both energy and information, some part of which is necessarily non-local. The author feels that quantum-mechanical systems take on aspects of computing engines, in this context. He discusses how the onset of chaos is possible with even the simplest calculational processes, how these processes also result in complexity building, and why both of these dynamics contribute to the character of entropy as observed in ordinary affairs, or with macroscopic systems.
Abstract. Both researchers and educators have expressed displeasure with the definition of entropy as a measure of disorder. Instead, it is argued by Leff, Lambert, and others that the increase of entropy can be far more accurately described using terms such as ‘dispersal of energy, ’ ‘spreading and sharing of energy, ’ and ‘spatial and temporal spreading. ’ In decoherence theory, a similar metaphor is used to describe the phenomena involved with quantum non-locality, superposition, and entanglement. Specifically the wavefunction of a quantum entity, such as a sub-atomic particle or photon is not seen to collapse but rather is transferred through interactions to a system and/or its environment. This suggests there may be a common basis for entropy and non-locality. I explore the idea that energy is motive and extensive by nature, and that all its forms of expression involve motion, action, and propagation, which clearly leads to its being spread and shared when unconstrained, among the available microstates of its local system and the larger environment. Thus a single description, focusing on this universal quality of energy, explains both 2 nd Law entropy and quantum non-locality.
The notion that fundamental properties common to all energetic phenomena engender both thermodynamic entropy and quantum non-locality has been explored by the author in two previous papers, and a significant amount of research. This paper summarizes those results, including both ideas from those papers and more recent developments. The idea that entropy pertains to the dispersal – or spreading and sharing – of energy has been widely adopted in Chemistry texts, over the prior notion that entropy reflects disorder. However; the situation is very different in Physics where that question has been sidestepped by the adoption of a model based on information loss. The author believes it is time to re-visit this matter, as the tendency for energy to spread and be shared may be a fundamental property.
The surprising aspects of quantum information are due to two distinctly non-classical features of the quantum world: first, different quantum states need not be orthogonal and, second, quantum states may be entangled. Non-orthogonality leads to the blurring of classical distinctions. On the other hand, entanglement leads via non-locality to teleportation and other ``entanglement-assisted'' forms of communication that go beyond what is classically possible. In this article we attempt to understand these new possibilities via an analysis of the significance of entanglement for the basic physical concepts of a ``particle'' and a ``localized physical system''. Classical particles can be individuated on the basis of qualitative differences in their sets of properties. But in entangled states the ``particle labels'' of the quantum formalism usually do not pick out such sets of individuating particle properties. It is sometimes nevertheless possible to think in terms of individual particles, which may be localized; but we argue that in general the structure of quantum mechanics is at odds with such a particle interpretation. This finally leads us to the conclusion that quantum mechanics is best seen as not belonging to the category of space-time theories, in which physical quantities are functions on space-time points. The resulting picture of the quantum world is relevant for our understanding of the way in which quantum theory is non-local, and it sheds light on the novel aspects of quantum information.
This study explores the non-local phenomena arising from quantum entanglement (often referred to as non-locality). It investigates these phenomena through fundamental concepts of quantum information theory (QIT), particularly those involving quantum state superposition. The emergence of non-locality is discussed in connection with electron correlation from a chemical viewpoint, emphasizing both historical context and scientific significance. This phenomenon is analyzed using selected atomic and molecular test cases, providing insights into fundamental aspects of chemical systems and the processes they undergo. Ultimately, this work advances the emerging discipline of Quantum Information Chemistry (QIChem).
This paper introduces a novel definition of non-classical information entropy, rooted in the principles of statistical physics, particularly quantum mechanics. The core premise is that traditional information entropy, derived from classical probability theory, is insufficient to capture the essence of information within non-classical systems exhibiting phenomena such as superposition and entanglement. We propose a definition based on the concept of accessible states and their associated probabilities, extending the notion of entropy beyond the realm of purely deterministic systems. The paper details the mathematical formulation of this non-classical information entropy, denoted as *Hnc*, and presents a method for its calculation. The method relies on identifying the set of accessible states for a given system and then applying a generalized form of Shannon's entropy formula, modified to account for the inherent uncertainties associated with quantum mechanics. The resulting *Hnc* provides a quantitative measure of the information content within non-classical systems, offering a potential framework for studying information processing and dynamics in quantum environments. The key contribution lies in bridging the gap between information theory and non-classical statistical physics, offering a new lens through which to understand information in quantum systems.
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy dynamics. This reveals a direct link with the theory of quantum chaotic systems, which can be characterized by a positive entropy production. Furthermore, noise, which inevitably affects any quantum system, can be modeled by a random quantum operation or by coupling to an environment in a generic chaotic state. In this contribution, we emphasize the universality of quantum chaotic dynamics and discuss its implications for quantum information processing.