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Journal of Information Technology & Software Engineering

Thermodynamic and Quantum Mechanical Limitations of Electronic Computation

Fayez Fok Al Adeh

Published Jan 1, 2016• 2 citations
Publisher

Abstract

The role of entropy and uncertainty in electronic computations is used to derive a fundamental thermodynamic equation. The thermodynamic limitations of electronic computations are expressed in terms of macroscopic disorder, while quantum mechanical limitations are formulated through uncertainty relationships. Electronic computations are described quantum-mechanically, and hence provide a reasonable argument in favour of the wave interpretation of quantum mechanics.

DOI
10.4172/2165-7866.1000187

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The role of entropy and uncertainty in electronic computations is used to derive a fundamental thermodynamic equation. The thermodynamic limitations of electronic computations are expressed in terms of macroscopic disorder, while quantum mechanical limitations are formulated through uncertainty relationships. Electronic computations are described quantum-mechanically, and hence provide a reasonable argument in favour of the wave interpretation of quantum mechanics.
In this communication new concept like the degree of assignment, the mass specific degree of assignment and a dynamic computer were introduced using concepts like second law of thermodynamics, Heisenberg’s uncertainty principle and entropy. The result formulated asserts that electronic computations are not out of the grasp of the second law of thermodynamics. Using Heisenberg’s uncertainty principle it is concluded that the total mass equivalent of the energy that is invested in signals communicating different elements of the computer cannot exceed the total mass of the system. While discussing quantum mechanical description main properties of algorithms and floating point numbers were used to provide a reasonable argument in favor of the wave interpretation of quantum mechanics as compared with other interpretations of quantum mechanics.
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This paper investigates the limits of quantum computing by applying the entropy increase principle from quantum state thermodynamics. We analyze the fundamental challenges posed by energy dissipation and information loss during quantum computations, leveraging the second law of thermodynamics. Specifically, we explore the implications of entropy generation on quantum coherence and fidelity, and propose theoretical frameworks for mitigating these effects. The core argument centers on demonstrating that inherent entropy generation processes, when unchecked, inevitably lead to the degradation of quantum states and ultimately limit the scalability of quantum computers. We formulate key mathematical expressions relating entropy generation rates to quantum gate operations and decoherence models. The analysis reveals that while quantum computation offers potential advantages, a thorough understanding and strategic management of entropy are crucial for realizing its full potential. The work highlights the necessity of robust error correction and innovative quantum architectures designed to minimize entropy generation. Furthermore, we explore the theoretical boundaries imposed by the second law of thermodynamics on the achievable fidelity of quantum computations.
The prevailing beliefs in the scientific and engineering literature are that: (i) thermodynamics is explained and justified by statistical mechanics; (ii) entropy is a statistical measure of disorder; and (iii) for given values of energy, volume, and amounts of constituents, the largest value of entropy corresponds to both a thermodynamic equilibrium state and the ultimate disorder. In this paper, we provide: (i) a summary of the beliefs as stated by some eminent scientists; (ii) experimental evidence that casts serious doubt about the validity of the beliefs; (iii) an outline of a nonstatistical unified quantum theory of mechanics and thermodynamics; (iv) an outline of a nonquantal, nonstatistical exposition of thermodynamics, valid for all systems (both macroscopic and microscopic), and for all states (both thermodynamic equilibrium and not thermodynamic equilibrium); (v) the definition and analytical expression of the entropy of thermodynamics; (vi) the interpretation of entropy as both a measure of the quantum-theoretic spatial shape of a molecule, and an indicator of order; and (vii) nonstatistical answers to the questions that motivated the introduction of statistical mechanics.
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This is intended to be an introductory book on information entropy. The concept of information theory is too broad to be captured by single definition. The term entropy is used in information theory to describe the amount of uncertainty. The information entropy is a fundamental quantity, related to thermodynamical entropy, which measures the extent of single particle density. The information and entropy both depend upon the choice of probability distribution. Quantum information science will lead to the creation of a quantum computer to solve problem that could not be solved by classical computer. The ideas from information theory have been applied to many problems of science and technology and in other different fields. Quantum Information entropy plays a crucial role in stronger formulation of uncertainty relation. The quantum information entropy of some important potentials is discussed which are widely used in different fields. The information entropy of these potentials is studied in position as well as momentum space and uncertainty relations are verified.