C. H. Bennett. Thermodynamics of computation---a review. International Journal of Theoretical Physics, 21:905--940, 12 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a careful delineation of the subjective and objective parts. A case in point is provided by E. T. Jaynes [18 20] insistence that entropy is a subjective quantity, a measure of ignorance about a physical system. One of the many fruits of this point of view can be found in the de nitive solution [21] to the long standing Maxwell demon problem [22] where it was realized that the information collected by a demon and used by it to extract work from heat has a thermodynamic cost at least as large as the work extracted [23] The example analyzed in detail in this paper provides another case. ....

C. H. Bennett, \The Thermodynamics of Computation|A Review," Int. J. Theor. Phys. 21, 905 (1982).

....finding a particle, fa = cos #. Provided photons do not escape to infinity. In this paper we use irreversibility, for practical purposes, in part of the quantum mechanical algorithm. By restricting oneself to reversible algorithms, in principle heat production may be avoided altogether [15, 16]. understanding we write (1) as #(t #)# = e #(t)#. 2) In this way the computational time advances incrementally in unit steps of duration # . Of course the state of the quantum computer exists at all intermediate times, say at t 2 , but for our purposes we need only use the state ....

Bennett, C.H.: Thermodynamics of computation---a review. Inter. J. of Theor. Phys., 21 (1982) 219--253

....of information about the initial value of the automaton can be traced back to many to one operations [26] di#erent states are mapped onto a single state with the same output. Many to one operations such as deletion of information are the only source of entropy increase in mechanistic systems [26, 27]. The reader is refered to much more detailed accounts in refs. 2, 28, 7] 3 Principle of self consistency Let us assume, for the rest of the article, that the universe is clocklike. In this part we shall review consequences of the basic and most evident consistency requirement that ....

Charles H. Bennett. The thermodynamics of computation---a review. In International Journal of Theoretical Physics [38], pages 905--940. Reprinted in [38, pp. 213-248].

....et al. are implementable in these same languages only when the inverses are likewise deterministic. Program version is an important and useful concept within di#erent software disciplines. Some representative theoretical papers on Turing machine inversion and reversible cellular automata are [McC56, Ben73, Ben82, TN90]. Broy uses program inverses to simplify the derivation of particular types of recursive structures during program synthesis [BKB80] Inversion is used in functional programming environments, such as Lisp [Kor81] fold and unfold transformation systems [Dar81] and Hope [HH86] Programming ....

C.H. Bennett. The thermodynamics of computation -- a review. International Journal of Theoretical Physics, 21(12):905--940, 1982.

....nevertheless largely ignored by both formalists and computationalists. On the other hand, hardware designers are acutely aware of the practical physical limits of speed, reliability and dissipation. Theories of reversible (dissipationless) computation have been proposed over the last few decades [3,28], but they are essentially thought experiments with idealized dynamical constraints. No one knows how to build a useful programmable computer along these lines. Bennett, 4] argues that the source of irreversibility in measurement is erasure rather than the measurement itself. This interpretation ....

Bennett, C. H., 1982, The thermodynamics of computation - a review, Int. d. Theor. Phys. 21,905-940.

....backward by inserting the output as new input, thereby obtaining the input one started with. In more formal terms, reversible computation can be characterized by one to one operations; i.e. by a reversible, bijective evolution of the computer states onto themselves [Lan61, Ben73, FT82, Ben82, Lan94, LH90] If only a finite number of such states are involved, this amounts to their permutation. For such a restricted regime, many to one operations such as deletion of bits or one to many operations such as copying are not allowed. The flow diagram depicted in Fig. 1 was introduced by ....

Bennett, C. H., The thermodynamics of computation---A review, International Journal of Theoretical Physics, (1982), 905--940 [Reprinted in LR90, pp. 213--248].

....Dept. of Computer Science, UCSD x Department of Computer Science, Hebrew University 1 in what ways this reversibility condition is indeed a true requirement, but rather limit ourselves to study models in which this requirement holds. The reader can consult for example Landauer[11] and Bennett[3, 4, 5] for more discussion. Our model of reversible computation will be boolean circuits which may use only reversible gates. Definition 1 A function g : f0; 1g k f0; 1g k is called reversible if it is 1 1 (thus, a permutation) A gate with k inputs and k outputs is called reversible if it ....

C.H. Bennett. The thermodynamics of computation - a review. International Journal of Theoretical Physics, 21(12):905, 1982.

....one of the longstanding problems of physics: the paradox of Maxwell s demon. What prevents the demon from breaking the second law of thermodynamics is the fact that it must erase the record of one measurement to make room for the next, and we know that such a process is physically irreversible [3]. In particular, the reversible techniques of this paper do not apply to the demon s calculation because it is permitted only one bit of scratchpad memory. The physics of computation has gained interest as e orts directed to apply quantum theory to computation have proved successful and with ....

Charles H. Bennett. The thermodynamics of computation - a review. IBM Journal of Research and Development, 21:905-940, 1981.

....if the simulated Turing Machine runs in time T , then after O(log T ) operations the simulation will produce a tube containing strings S o S f where S o encodes the initial configuration and S f a final configuration. Other papers have also addressed the problem of Turing Machine simulation (see [14, 68, 13], for example, and [22] for a review of some of these models) 3.5 Constructive models An important area of enquiry that is outstanding is the quest for algorithms which proceed through polynomial sized sets of strings (i.e. volumes of DNA) It is clear that the naive, filtering approach will ....

C. H. Bennett. The thermodynamics of computation -- a review. International Journal of Theoretical Physics, 21:905--940, 1982.

....environment. With computational device technology rapidly approaching the elementary particle level it has been argued many times that this effect gains in significance to the extent that efficient operation (or operation at all) of future computers requires them to be reversible (for example, in [8, 1, 2, 4, 7, 11, 5]) The mismatch of computing organization and reality will express itself in friction: computers will dissipate a lot of heat unless their mode of operation becomes reversible, possibly quantum mechanical. Since 1940 the dissipated energy per bit operation in a computing device has with ....

C.H. Bennett. The thermodynamics of computation---a review. Int. J. Theoret. Phys., 21(1982), 905-940.

.... need be consumed (except for retaining the answer) Basically normal computation increases disorder (i.e. entropy) and is irreversible, but a reversible design does not increase disorder (the reverse action acts like a refrigerator) This fundamental concept was further developed by Bennett [1, 2, 3] who showed it was possible to construct a modified form of Turing machine which was reversible, and hence that any computation is potentially reversible. In a later development Fredkin [6] showed that it was possible to construct a conservative logic gate which was reversible but could be used ....

C.H. Bennett, "The Thermodynamics of Computation, a Review", International Journal of Theoretical Physics, vol. 21, pp. 905--940, 1982

....the bu#er (or inverter) shown in Fig. 2 is basically reversible, most of the Boolean gates are not reversible. Note that mapping from the input to the output must be always one to one to be a reversible logic gate. As many Boolean functions require garbage information to make them reversible [9], there is some circuit overhead due to reversibility. The output in an RERL full adder contains garbage information for reversibility such as X and C in , as shown in Fig. 5, which are delayed copies of the input signals X and C in , respectively. Similarly, we can make any Boolean function a ....

C.H. Bennett, "The thermodynamics of computation---A review," Int. Journal of Theoretical Physics, vol.21, no.12, pp.905--940, 1982.

....: 83 6.2 Energy measurements for rail FF3( and RF4( in SCRL 1. 84 viii Part I Introduction and Background 1 1. Introduction 1. 1 New Ideas, Old Physics In principle, a computing engine need not dissipate any energy as shown in the work of Bennett, Feynman, and Landauer [3] [11] 27] Although these authors approach the problem from different disciplines and use different physical as well as theoretical models, they all conclude that the transfer of energy through a dissipative medium dissipates arbitrarily small amounts of energy if that transfer is made ....

Bennett, C., "The Thermodynamics of Computation -- a Review", International Journal of Theoretical Physics, Vol. 21, No. 12, 1982, pages 905-940.

.... of computation on a 4 Even before quantum mechanics becomes a constraint, the reversibility of lattice gas dynamics may become a significant benefit, since at very high logic densities the dissipation of heat caused by irreversible computations has already become an important engineering issue [8, 9]. 10 discrete spacetime lattice, Feynman noticed the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature [37] He hoped that using computers in an exactly computable way might lead to new possibilities in our understanding of physics. ....

Charles H. Bennett. Thermodynamics of computation---a review. International Journal of Theoretical Physics, 21:219--253, 1982.

....Distance Reversible models of computation in which the transition function is one to one have been explored especially in connection with the question of the thermodynamic limits of computation. Reversible Turing machines were introduced by Lecerf [18] and independently but much later by Bennett [3, 4]. Further results concerning them can be found in [4, 5, 19, 20] Consider the standard model of Turing machine. The elementary operations are rules in quadruple format (p; a; b; q) meaning that a machine in state p scanning symbol a writes a symbol or moves the scanning head one square left, one ....

....transition function is one to one have been explored especially in connection with the question of the thermodynamic limits of computation. Reversible Turing machines were introduced by Lecerf [18] and independently but much later by Bennett [3, 4] Further results concerning them can be found in [4, 5, 19, 20]. Consider the standard model of Turing machine. The elementary operations are rules in quadruple format (p; a; b; q) meaning that a machine in state p scanning symbol a writes a symbol or moves the scanning head one square left, one square right, or not at all (as indicated by b) and enters ....

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C.H. Bennett. The thermodynamics of computation---a review. Int'l J. Theoret. Physics, 21:905--940, 1982.

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C. H. Bennett. Thermodynamics of computation---a review. International Journal of Theoretical Physics, 21:905--940, 12 1982.

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Bennett, C.H. The thermodynamics of computation ---A review. Int. J. Theor. Phys. 1982, 21 (12), 905 -- 940.

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C. H. Bennett, The thermodynamics of computation---a review,Int. J. Theoretical Physics, 21 (1982), pp. 905--940.

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C. H. Bennett, `The thermodynamics of computation--a review', International Journal of Theoretical Physics 21 (1982.), no. 905-940.

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Bennett, C. The thermodynamics of computation { a review. Int J. Theoret. Phys 21 (1982), 905-940.

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C. H. Bennett. Thermodynamics of computation---a review. International Journal of Theoretical Physics, 21:905--940, 12 1982.

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C. H. Bennett. The thermodynamics of computation|a review. Int. J. Theoret. Phys., 21:905-940, 1982.

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Bennett C H, The Thermodynamics of Computation - a Review, International Journal of Theoretical Physics, 21, No. 12, p 905, 1982

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Charles H. Bennett. Thermodynamics of computation---a review. International Journal of Theoretical Physics, 21:219--253, 1982.

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Charles H. Bennett. The thermodynamics of computation -- a review. International Journal of Theoretical Physics, 21(12):905--940, 1982.

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