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Thermodynamics of Computation

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Book cover Computational Complexity

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Article Outline

Glossary

Definition of the Subject

Introduction

Thermodynamics

Computer Equivalents of the First and Second Laws

The Thermodynamics of Digital Computers

Analog and Digital Computers

Natural Computing

Quantum Computing

Optical Computing

Thermodynamically Inspired Computing

Cellular Array Processors

Conclusions

Future Directions

Bibliography

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Abbreviations

Thermodynamics:

Literally accounting for the impact of temperature and energy flow. It is a branch of physics that describes how temperature, energy, and related properties affect behavior of an object or event.

First law of thermodynamics:

Also known as the law of energy conservation. It states that the energy remains constant in an isolated system.

Second law of thermodynamics:

The second law of thermodynamics asserts that the entropy of an isolated system never decreases with time.

Entropy:

A measure of the disorder or unavailability of energy within a closed system.

Computing:

Any activity with input/output patterns mapped onto real problems to be solved.

Turing machine:

An abstract computing model that was invented by Alan Turing in 1936, long before the first electronic computer was invented, to serve as an idealized model for computing. A Turning machine has a tape that is unbounded in both directions, a read‐write head and a finite set of instructions. At each step, the head may modify the symbol on the tape right under the head, change the state of the head, and then move on the tape one unit to the left or right. Although extremely simple, Turing machines can solve any problem that can be solved by any computers that could possibly be constructed (see Church–Turing thesis).

The Church–Turing thesis:

A combined hypothesis about the nature of computable functions. It states that any function that is naturally regarded as computable is computable by a Turing Machine. In early 20th century, various computing models such as Turing Machine, λ‑calculus and recursive functions are invented. It was proved that Turing Machine, λ‑calculus and recursive functions are equally powerful. Alonzo Church and Alan Turing independently raised the thesis that any naturally computable function must be a recursive function or, equivalently, be computed by a Turing Machine, or be a λ‑definable function. In other words, it is not possible to build a computing device that is more powerful than those machines with simplest computing mechanisms. Note that Church–Turing thesis is not a provable or refutable conjecture because “naturally computable function” is not a rigorous definition. There is no way to prove or refute it. But it has been accepted by nearly all mathematicians today.

Analog:

An analog computer is often negatively defined as a computer that is not digital. More properly, it is a computer that uses quantities are that can be made proportional to the amount of signal detected. That analogy between a real number and a physical property gives the name “analog.” Many problems arise in analog computing, because it is so difficult to obtain a large number of distinguishable levels and because noise builds up in cascaded computations. But, being unencoded, it can always be run faster than its digital counterpart.

Digital:

The name derives from digits (the fingers). Digital computing works with discrete items like fingers. Most digital computing is binary – using 0 and 1. Because signals are restored to a 1 or a 0 after each operation, noise accumulation is not much of a problem. And, of course, digital computers are much more flexible than analog computers that tend to be rather specialized.

Quantum computer:

A quantum computer is a computing device that makes direct use of quantum mechanical phenomena such as superposition and entanglement. Theoretically, quantum computers can achieve much faster speed than traditional computers. It can solve some NP hard or even exponentially hard problem within linear time. Due to many technical difficulties, no practical quantum computer using entanglement has been built up to now.

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Author information

Authors and Affiliations

  1. Fisk University, Nashville, USA

    H. John Caulfield & Lei Qian

Authors
  1. H. John Caulfield
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  2. Lei Qian
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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© 2012 Springer-Verlag

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Caulfield, H.J., Qian, L. (2012). Thermodynamics of Computation. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_197

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