# The thermodynamics of computation—a review

@article{Bennett1982TheTO,
title={The thermodynamics of computation—a review},
author={Charles H. Bennett},
journal={International Journal of Theoretical Physics},
year={1982},
volume={21},
pages={905-940}
}
• C. H. Bennett
• Published 1 December 1982
• Physics
• International Journal of Theoretical Physics
Computers may be thought of as engines for transforming free energy into waste heat and mathematical work. Existing electronic computers dissipate energy vastly in excess of the mean thermal energykT, for purposes such as maintaining volatile storage devices in a bistable condition, synchronizing and standardizing signals, and maximizing switching speed. On the other hand, recent models due to Fredkin and Toffoli show that in principle a computer could compute at finite speed with zero energy…
1,356 Citations

## Figures from this paper

The Power of Being Explicit: Demystifying Work, Heat, and Free Energy in the Physics of Computation
• Physics, Computer Science
The Energetics of Computing in Life and Machines
• 2019
This chapter addresses widespread misconceptions about thermodynamics and the thermodynamics of computation, and analyses these ideas via an explicit biochemical representation of the entire cycle of Szilard's engine, showing that molecular computation is both a promising engineering paradigm, and a valuable tool in providing fundamental understanding.
Mechanical Autonomous Stochastic Heat Engine.
• Physics, Medicine
Physical review letters
• 2016
This work presents a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive that presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Physics of computation: tightness of timing vs. heat generated
• Computer Science, Engineering
SPIE Defense + Commercial Sensing
• 2001
It is shown not to mix with quantum superposition expressed by the quantum dynamics of a Schrodinger equation, which precludes so-called quantum computers from producing super-linear speed-up at a scale large enough to be useful, and clarifies a conceptual separation between digital computing and devices exhibiting quantum phase sensitivity.
The thermodynamic cost of quantum operations
• Physics
• 2016
The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate
Minimising the heat dissipation of information erasure
• 2015
Quantum state engineering and quantum computation rely on procedures that, up to some fidelity, prepare a quantum object in a pure state. If the object is initially in a statistical mixture, then
Thermodynamics of quasideterministic digital computers.
• D. Chu
• Computer Science, Physics
Physical review. E
• 2018
Using a thermodynamically consistent model, it is shown that quasideterministic computation can be achieved at finite, and indeed modest cost with accuracies that are indistinguishable from deterministic behavior for all practical purposes.
Quantum Mechanical Hamiltonian Models of Computers a
Interest in the physical limitations of the computation process has been increasing in recent years.’.’ Landauer3“ has discussed this subject extensively, particularly from the viewpoint of energy
A quantum Szilard engine without heat from a thermal reservoir
• Physics
• 2017
We study a quantum Szilard engine that is not powered by heat drawn from a thermal reservoir, but rather by projective measurements. The engine is constituted of a system $\mathcal{S}$, a weight
Thermodynamics of Error Correction
• Computer Science, Biology
• 2015
A universal expression for the copy error as a function of entropy production and cred work dissipated by the system during wrong incorporations is derived and it is shown that, for any effective proofreading scheme, error reduction is limited by the chemical driving of the proofreading reaction.
Experimental verification of Landauer’s principle linking information and thermodynamics
• Medicine
Nature
• 2012
It is established that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles, demonstrating the intimate link between information theory and thermodynamics and highlighting the ultimate physical limit of irreversible computation.

## References

SHOWING 1-10 OF 29 REFERENCES
Minimal energy dissipation in logic
• Mathematics
• 1970
Minimal energy dissipations for the logic process based on thermodynamics and general phase space considerations are known. The actual availability of these minimal dissipations has not, however,
Conservative logic
• 1982
Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the
Logical reversibility of computation
This result makes plausible the existence of thermodynamically reversible computers which could perform useful computations at useful speed while dissipating considerably less than kT of energy per logical step.
Classical and quantum limitations on energy consumption in computation
Fundamental limitations on the energy dissipated during one elementary logical operation are discussed. A model of a real physical device (parametric quantron) based on the Josephson effect in
The Inversion of Functions Defined by Turing Machines
This paper deals with the problem of designing a Turing machine which, when confronted by the number pair, computes as efficiently as possible a function g(m, r) such that fm(g( m, r)) = r.
Reversible Computing
According to a physical interpretation, the central result of this paper is that i¢ is ideally possible to build sequential c/rcuits with zero internal power dissipation.
THE COMPLEXITY OF FINITE OBJECTS AND THE DEVELOPMENT OF THE CONCEPTS OF INFORMATION AND RANDOMNESS BY MEANS OF THE THEORY OF ALGORITHMS
• Mathematics
• 1970
In 1964 Kolmogorov introduced the concept of the complexity of a finite object (for instance, the words in a certain alphabet). He defined complexity as the minimum number of binary signs containing
Dissipation-error tradeoff in proofreading.
Chemical proofreading systems, of the kind believed responsible for the extremely high fidelity of DNA replication, achieve minimum error probability only in the limit of infinite energy dissipation.
Efficient estimation of free energy differences from Monte Carlo data
Abstract Near-optimal strategies are developed for estimating the free energy difference between two canonical ensembles, given a Metropolis-type Monte Carlo program for sampling each one. The
Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity.
• J. Hopfield
• Biology, Medicine
Proceedings of the National Academy of Sciences of the United States of America
• 1974
The specificity with which the genetic code is read in protein synthesis, and with which other highly specific biosynthetic reactions take place, can be increased above the level available from free