Irreversibility and heat generation in the computing process
Abstract
It is argued that computing machines inevitably involve devices which perform logical functions that do not have a single-valued inverse. This logical irreversibility is associated with physical irreversibility and requires a minimal heat generation, per machine cycle, typically of the order of kT for each irreversible function. This dissipation serves the purpose of standardizing signals and making them independent of their exact logical history. Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.
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Landauer's bound gives the minimal energy required to perform an abstract computation and many string writing operations, including copies and transformations.
“Landauer’s bound [132] gives us the minimal energy required to perform an abstract computation and many string writing operations, including copies and transformations of it [133].”
From Fundamental constraints to the logic of living systems (2024) · cites this paper as [132]
The ordering Simp(t1)<Simp(t2) is frame-invariant and defines the QMM arrow of time.
“Hence, Simp supplies an intrinsic clock; the ordering Simp(t1)<Simp(t2) is frame-invariant and defines the QMM arrow of time [28,29].”
From Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe (2025) · cites this paper as [28]
Classically one may delete one copy against the others, uncopying it in a perfectly reversible manner.
“Classically we may delete one copy against the others, uncopying it in a perfectly reversible manner 7 .”
From Impossibility of deleting an unknown quantum state (2000) · cites this paper as [7]
Erasing a single copy of some classical information is an irreversible operation.
“As is now well understood, erasing a single copy of some classical information is an irreversible operation.”
From Impossibility of deleting an unknown quantum state (2000) · cites this paper as [7]
Erasing a single copy of classical information may only be done with some energy cost, known as the Landauer erasure principle.
“It may only be done with some energy cost; a result known as the Landauer erasure principle 7 .”
From Impossibility of deleting an unknown quantum state (2000) · cites this paper as [7]
Landauer established that erasing a single bit of information has a minimum energetic cost given by the dissipated heat Q = k_B T ln 2.
“In particular, Landauer established that in order to erase a single bit of information there is an associated minimum energetic cost, given by the dissipated heat [270,271] Q = k B T ln 2.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [270]
Landauer showed that reversible, one-to-one logical operations such as NOT can be performed without dissipation in principle, but irreversible, many-to-one operations such as AND or ERASE require dissipation at least kB ln 2 for each bit of information lost.
“The precise, correct statement of the role of entropy in computation was due to Landauer 5 , who showed that reversible, i.e. one-to-one, logical operations such as NOT can be performed without dissipation in principle, but that irreversible, many-to-one operations such as AND or ERASE require dissipation at least k B ln 2 for each bit of information lost.”
From Ultimate physical limits to computation (2000) · cites this paper as [5]
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- Authors
- Landauer, R.
- Corresponding author
- Landauer, R.
- Venue
- IBM Journal of Research and Development
- Publisher
- IBM
- Published
- 1961-07
- Volume
- 5
- Issue
- 3
- Pages
- 183-191
- ISSN
- 0018-8646 (ISSN-L)
- OpenAlex
- W4233798822
- Cited by
- 4,980
- References
- 0
- Citations by year
- 2026: 367 · 2025: 314 · 2024: 278 · 2023: 327 · 2022: 262 · 2021: 298 · 2020: 272 · 2019: 243 · 2018: 267 · 2017: 274 · 2016: 241 · 2015: 219 · 2014: 235 · 2013: 188 · 2012: 157
- FWCI
- 4.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IBM Journal of Research and Development (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Quantum-Dot Cellular Automata
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Keywords
- heat generation, energy dissipation, computing machines, bistable devices, switching kinetics, thermal fluctuations
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