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Entropy
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Physical Information and the Physical Foundations of Computation
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Physical Information and the Physical Foundations of Computation

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 23295

Special Issue Editor

Prof. Neal G. Anderson

E-Mail Website
Guest Editor
Department of Electrical & Computer Engineering, University of Massachusetts Amherst, Amherst, MA 01003-9292, USA
Interests: fundamental physical understanding of information and computation, physical-information theories, energy efficiency of computation, fundamental physical limits in computation, post-CMOS nanocomputing and other unconventional and natural computing paradigms

Special Issue Information

Dear Colleagues,

Nearly six decades have passed since Landauer declared that “information is physical” and proposed a fundamental thermodynamic link between information erasure and heat generation in computing processes. While Landauer’s ideas have been extensively analyzed, interpreted, and critiqued from multiple perspectives and have been generalized and extended within various physical theories of information and computation, they remain stubbornly controversial. This is a symptom of a broader and somewhat ironic predicament: Deep in this information age, we have highly sophisticated and widely used models of computing machines as physical systems, but we remain without a comprehensive and widely accepted fundamental understanding of computation as a distinct physical process with information as its physical currency. Without such an understanding, we cannot expect consensus resolution of contested claims associated with the physicality of information or, more generally, claim an established physical foundation for computation.

This Special Issue aims to clarify and advance the physical understanding of information and computation. We invite a broad range of original, high-quality contributions from a variety of disciplinary perspectives—including but not limited to engineering, physics, computer science, neuroscience, information science, biological physics, and the philosophy of science—that explicitly address fundamental links between physics, information, and computation. Submissions are welcome on all topics that serve to clarify and illuminate the physical dimensions of information and computation, codify them in physical definitions and theories, and reveal their consequences and implications.

Prof. Neal G. Anderson
Guest Editor

Manuscript Submission Information 

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropyis an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions. For invited papers by the Guest Editor which are submitted before 31 December 2020, we can apply a discount of 200 CHF. Please also note that for papers submitted after 31 December 2020 an APC of 1800 CHF applies.

Keywords

  • Physical conceptions, definitions, and measures of information (entropic and otherwise)
  • Physical conceptions, definitions, and measures of computation (thermodynamic and otherwise)
  • Physical information in specific computing contexts (digital, analog, natural, reversible, quantum, neural)
  • Distinctions between physical dynamics, information processing, and computation
  • Observer- and user-dependent notions of information and computation and their formal physical description
  • Fundamental physical limits and resource requirements for computation
  • Fluctuations and noise in physical information and computation
  • New perspectives on Landauer’s Principle, Maxwell’s Demon, and other controversial issues, including paths toward resolution
  • Other topics that explicitly address links between physics, information, and computation, including substantiated denials of such links

Published Papers (9 papers)

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Research

15 pages, 278 KiB  
Article
Generalized Landauer Bound for Information Processing: Proof and Applications
by Neal G. Anderson
Entropy 2022, 24(11), 1568; https://0-doi-org.brum.beds.ac.uk/10.3390/e24111568 - 31 Oct 2022
Viewed by 1169
Abstract
A generalized form of Landauer’s bound on the dissipative cost of classical information processing in quantum-mechanical systems is proved using a new approach. This approach sidesteps some prominent objections to standard proofs of Landauer’s bound—broadly interpreted here as a nonzero lower bound on [...] Read more.
A generalized form of Landauer’s bound on the dissipative cost of classical information processing in quantum-mechanical systems is proved using a new approach. This approach sidesteps some prominent objections to standard proofs of Landauer’s bound—broadly interpreted here as a nonzero lower bound on the amount of energy that is irreversibly transferred from a physical system to its environment for each bit of information that is lost from the system—while establishing a far more general result. Specializations of our generalized Landauer bound for ideal and non-ideal information processing operations, including but not limited to the simplified forms for erasure and logical operations most familiar from the literature, are presented and discussed. These bounds, taken together, enable reconsideration of the links between logical reversibility, physical reversibility, and conditioning of operations in contexts that include but are far more general than the thermodynamic model systems that are most widely invoked in discussions of Landauer’s Principle. Because of the strategy used to prove the generalized bounds and these specializations, this work may help to illuminate and resolve some longstanding controversies related to dissipation in computation. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
157 pages, 7548 KiB  
Article
Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
by Huan-Qiang Zhou, Qian-Qian Shi and Yan-Wei Dai
Entropy 2022, 24(9), 1306; https://0-doi-org.brum.beds.ac.uk/10.3390/e24091306 - 15 Sep 2022
Cited by 5 | Viewed by 1831
Abstract
Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us [...] Read more.
Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin-1/2 XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-1/2 XYZ model, the quantum spin-1/2 XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-1/2 Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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25 pages, 6064 KiB  
Article
Thermodynamic State Machine Network
by Todd Hylton
Entropy 2022, 24(6), 744; https://0-doi-org.brum.beds.ac.uk/10.3390/e24060744 - 24 May 2022
Cited by 3 | Viewed by 2172
Abstract
We describe a model system—a thermodynamic state machine network—comprising a network of probabilistic, stateful automata that equilibrate according to Boltzmann statistics, exchange codes over unweighted bi-directional edges, update a state transition memory to learn transitions between network ground states, and minimize an action [...] Read more.
We describe a model system—a thermodynamic state machine network—comprising a network of probabilistic, stateful automata that equilibrate according to Boltzmann statistics, exchange codes over unweighted bi-directional edges, update a state transition memory to learn transitions between network ground states, and minimize an action associated with fluctuation trajectories. The model is grounded in four postulates concerning self-organizing, open thermodynamic systems—transport-driven self-organization, scale-integration, input-functionalization, and active equilibration. After sufficient exposure to periodically changing inputs, a diffusive-to-mechanistic phase transition emerges in the network dynamics. The evolved networks show spatial and temporal structures that look much like spiking neural networks, although no such structures were incorporated into the model. Our main contribution is the articulation of the postulates, the development of a thermodynamically motivated methodology addressing them, and the resulting phase transition. As with other machine learning methods, the model is limited by its scalability, generality, and temporality. We use limitations to motivate the development of thermodynamic computers—engineered, thermodynamically self-organizing systems—and comment on efforts to realize them in the context of this work. We offer a different philosophical perspective, thermodynamicalism, addressing the limitations of the model and machine learning in general. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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68 pages, 3761 KiB  
Article
Quantum Foundations of Classical Reversible Computing
by Michael P. Frank and Karpur Shukla
Entropy 2021, 23(6), 701; https://0-doi-org.brum.beds.ac.uk/10.3390/e23060701 - 01 Jun 2021
Cited by 4 | Viewed by 5553
Abstract
The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for, and analysis of, [...] Read more.
The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for, and analysis of, classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer’s Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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16 pages, 3006 KiB  
Article
Physical Limitations on Fundamental Efficiency of SET-Based Brownian Circuits
by İlke Ercan, Zeynep Duygu Sütgöl and Faik Ozan Özhan
Entropy 2021, 23(4), 406; https://0-doi-org.brum.beds.ac.uk/10.3390/e23040406 - 30 Mar 2021
Cited by 1 | Viewed by 2124
Abstract
Brownian circuits are based on a novel computing approach that exploits quantum fluctuations to increase the efficiency of information processing in nanoelectronic paradigms. This emerging architecture is based on Brownian cellular automata, where signals propagate randomly, driven by local transition rules, and can [...] Read more.
Brownian circuits are based on a novel computing approach that exploits quantum fluctuations to increase the efficiency of information processing in nanoelectronic paradigms. This emerging architecture is based on Brownian cellular automata, where signals propagate randomly, driven by local transition rules, and can be made to be computationally universal. The design aims to efficiently and reliably perform primitive logic operations in the presence of noise and fluctuations; therefore, a Single Electron Transistor (SET) device is proposed to be the most appropriate technology-base to realize these circuits, as it supports the representation of signals that are token-based and subject to fluctuations due to the underlying tunneling mechanism of electric charge. In this paper, we study the physical limitations on the energy efficiency of the Single-Electron Transistor (SET)-based Brownian circuit elements proposed by Peper et al. using SIMON 2.0 simulations. We also present a novel two-bit sort circuit designed using Brownian circuit primitives, and illustrate how circuit parameters and temperature affect the fundamental energy-efficiency limitations of SET-based realizations. The fundamental lower bounds are obtained using a physical-information-theoretic approach under idealized conditions and are compared against SIMON 2.0 simulations. Our results illustrate the advantages of Brownian circuits and the physical limitations imposed on their SET-realizations. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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22 pages, 2327 KiB  
Article
Conditional Action and Imperfect Erasure of Qubits
by Heinz-Jürgen Schmidt
Entropy 2021, 23(3), 289; https://0-doi-org.brum.beds.ac.uk/10.3390/e23030289 - 26 Feb 2021
Viewed by 1732
Abstract
We consider state changes in quantum theory due to “conditional action” and relate these to the discussion of entropy decrease due to interventions of “intelligent beings” and the principles of Szilard and Landauer/Bennett. The mathematical theory of conditional actions is a special case [...] Read more.
We consider state changes in quantum theory due to “conditional action” and relate these to the discussion of entropy decrease due to interventions of “intelligent beings” and the principles of Szilard and Landauer/Bennett. The mathematical theory of conditional actions is a special case of the theory of “instruments”, which describes changes of state due to general measurements and will therefore be briefly outlined in the present paper. As a detailed example, we consider the imperfect erasure of a qubit that can also be viewed as a conditional action and will be realized by the coupling of a spin to another small spin system in its ground state. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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25 pages, 509 KiB  
Article
Computational Abstraction
by Raymond Turner
Entropy 2021, 23(2), 213; https://0-doi-org.brum.beds.ac.uk/10.3390/e23020213 - 10 Feb 2021
Cited by 5 | Viewed by 1940
Abstract
Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure [...] Read more.
Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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15 pages, 1363 KiB  
Article
Coherence and Entanglement Dynamics in Training Variational Quantum Perceptron
by Min Namkung and Younghun Kwon
Entropy 2020, 22(11), 1277; https://0-doi-org.brum.beds.ac.uk/10.3390/e22111277 - 11 Nov 2020
Cited by 2 | Viewed by 2191
Abstract
In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum [...] Read more.
In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum perceptron proposed by Y. Du et al., arXiv:1809.06056 (2018). In detail, we show that in the first part of the training of the variational quantum perceptron, the quantum coherence of the total system is concentrated in the index register and in the second part, the Grover algorithm consumes the quantum coherence in the index register. This implies that the quantum coherence distribution and the quantum coherence depletion are required in the training of variational quantum perceptron. In addition, we investigate the behavior of entanglement during the training of variational quantum perceptron. We show that the bipartite concurrence between feature and index register decreases since Grover operation is only performed on the index register. Also, we reveal that the concurrence between the two qubits of index register increases as the variational quantum perceptron is trained. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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13 pages, 893 KiB  
Article
Blind Witnesses Quench Quantum Interference without Transfer of Which-Path Information
by Craig S. Lent
Entropy 2020, 22(7), 776; https://0-doi-org.brum.beds.ac.uk/10.3390/e22070776 - 16 Jul 2020
Viewed by 2291
Abstract
Quantum computation is often limited by environmentally-induced decoherence. We examine the loss of coherence for a two-branch quantum interference device in the presence of multiple witnesses, representing an idealized environment. Interference oscillations are visible in the output as the magnetic flux through the [...] Read more.
Quantum computation is often limited by environmentally-induced decoherence. We examine the loss of coherence for a two-branch quantum interference device in the presence of multiple witnesses, representing an idealized environment. Interference oscillations are visible in the output as the magnetic flux through the branches is varied. Quantum double-dot witnesses are field-coupled and symmetrically attached to each branch. The global system—device and witnesses—undergoes unitary time evolution with no increase in entropy. Witness states entangle with the device state, but for these blind witnesses, which-path information is not able to be transferred to the quantum state of witnesses—they cannot “see” or make a record of which branch is traversed. The system which-path information leaves no imprint on the environment. Yet, the presence of a multiplicity of witnesses rapidly quenches quantum interference. Full article
(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)
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