Does Erasing Information Cost Energy? Landauer’s Principle (and the Debate Around It)

When you empty your computer’s trash, the bits vanish and nothing seems to happen. But in 1961 the IBM physicist Rolf Landauer argued that erasing information has an unavoidable physical price: it must release a minimum amount of heat. That claim, now called Landauer’s principle, is the idea behind our Sortex sticker, a Maxwell’s-demon character who has to pay for every bit he forgets. This post builds on our explainer Why Does Time Only Go Forward?, because the principle is really a statement about the second law of thermodynamics.

What does Landauer’s principle say?

Landauer’s 1961 paper, “Irreversibility and Heat Generation in the Computing Process,” was published in the IBM Journal of Research and Development (Landauer 1961^[1]). The principle is usually stated like this: any logically irreversible operation on information, such as erasing a bit, must be accompanied by an entropy increase in the surroundings. Charles Bennett, who did more than anyone to develop the idea, phrases it as “any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase” in the apparatus or its environment (Bennett 2003^[2]).

For one bit at temperature T, the minimum work that must be turned into heat is

W ≥ k_B T ln 2

Here W is work in joules, k_B is the Boltzmann constant, exactly 1.380 649 × 10⁻²³ J/K (NIST^[3]), T is the absolute temperature in kelvin, and ln 2 ≈ 0.693 is the natural logarithm of 2, because one bit has two possible states.

A worked number

At room temperature, T = 300 K:

k_B T ln 2 = 1.380 649 × 10⁻²³ J/K × 300 K × 0.693 ≈ 2.87 × 10⁻²¹ J

That is about 0.018 electronvolts per bit. It is tiny. Erasing a full terabyte (8 × 10¹² bits) at this limit would release only about 2.3 × 10⁻⁸ J. Real computers dissipate far more per operation, so the Landauer limit is a floor, not a description of today’s hardware.

Why should erasing cost anything?

Think of a bit as a particle that can sit in either of two boxes, left (0) or right (1). If you do not know which box it is in, there are two possibilities. “Erasing” means resetting the bit to 0 no matter where it started. Afterwards there is only one possibility. You have shrunk the number of possible states by a factor of 2.

In statistical mechanics, entropy measures the number of possible microscopic arrangements, through Boltzmann’s formula S = k_B ln W (we cover it in What Is Entropy?). Halving the possibilities lowers the bit’s entropy by k_B ln 2. The second law does not allow total entropy to drop, so at least that much entropy has to go somewhere else, as heat Q = TΔS = k_B T ln 2 released into the surroundings.

The Stanford Encyclopedia of Philosophy describes the setup: resetting a one-molecule memory in contact with a heat bath requires “at least kT ln 2 work” by standard calculations, and Landauer’s principle is the claim that no physical implementation can do better (Maroney, SEP^[4]).

How does this solve Maxwell’s demon?

Maxwell’s demon first appeared in an 1867 letter from James Clerk Maxwell to P. G. Tait (Maroney, SEP^[4]). Maxwell imagined a tiny being that sorts fast and slow molecules between two chambers, apparently lowering entropy for free. For decades physicists tried to find where the demon pays. Bennett’s answer, building on Landauer, was that the demon must record each measurement, and to keep working with a finite memory it must eventually erase those records. The erasure produces at least as much entropy as the sorting removed. Bennett also argued that the other steps, measuring and computing, can in principle be done reversibly (Bennett 2003^[2]).

So the demon is not defeated by the cost of looking, but by the cost of forgetting. Sortex is the character for that bargain, and our Thermodynamics Pixel Sticker Sheet gathers more characters from the same corner of physics.

Has Landauer’s limit been measured?

Yes, in small systems, and with care about what is being measured.

• 2012. Antoine Bérut and colleagues trapped a single colloidal particle in a modulated double-well potential that worked as a one-bit memory. They found that “the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles” (Bérut et al. 2012^[5]). Fast erasures cost more; slow ones approached kT ln 2 from above.
• 2014, Simon Fraser University. Yonggun Jun, Momčilo Gavrilov and John Bechhoefer used a feedback trap and confirmed that reducing the number of states by a factor of 2 “requires work of at least kT ln 2”. They also found that in individual cycles the work “can be below the Landauer limit, consistent with the Jarzynski equality” (Jun, Gavrilov & Bechhoefer 2014^[6]).

That second point matters. The bound holds on average. Single small events fluctuate, sometimes below the limit, exactly as modern statistical mechanics predicts for tiny systems.

Is Landauer’s principle a law? (debated)

Here we have to be careful, because this is an open question in the foundations of physics. The experiments above match the predicted bound for the systems tested. What is argued over is the status of the principle itself.

• Critics. The philosopher of physics John D. Norton has argued that the general proofs offered for the principle fall short. The Stanford Encyclopedia notes later work responding “in part to Norton’s (2005) criticism of the generality of previous proofs of Landauer’s principle” (Norton 2005^[7]; Maroney, SEP^[4]). In a 2011 paper titled “Waiting for Landauer,” Norton continued the critique (Norton 2011^[8]).
• Defenders. Bennett wrote that the principle has been criticized “either as being false, or as being trivial and obvious” and set out to refute those arguments (Bennett 2003^[2]).
• Overall. The Stanford Encyclopedia’s summary is that attempts to settle these questions “have illustrated many open questions in the foundations of statistical mechanics” (Maroney, SEP^[4]).

A fair summary: as a working rule for the thermodynamics of small memories, the bound is well supported by experiment. Whether it is an independent fundamental principle, a consequence of the second law, or something that needs a cleaner general proof remains debated.

FAQ

Does deleting a file on my laptop release kT ln 2 per bit?

Your laptop releases vastly more heat than that per operation. The Landauer limit is the theoretical minimum for erasure, far below what current electronics use.

Can computing ever be free of energy cost?

Bennett argued that logically reversible computation can in principle be done with arbitrarily little dissipation, if run slowly enough. Only erasure carries the unavoidable cost.

Is information physical?

Stored information always lives in some physical system, a charge, a magnet or a trapped particle, and erasing it changes that system’s entropy. How much more follows from this is part of the debate above.

References

1. R. Landauer (1961), “Irreversibility and Heat Generation in the Computing Process,” IBM J. Res. Dev. 5, 183–191 (DOI 10.1147/rd.53.0183; metadata verified via Crossref). https://doi.org/10.1147/rd.53.0183
2. C. H. Bennett (2003), “Notes on Landauer’s principle, reversible computation, and Maxwell’s Demon,” Stud. Hist. Phil. Mod. Phys. 34, 501–510 (arXiv:physics/0210005). https://arxiv.org/abs/physics/0210005
3. NIST CODATA 2022 recommended values: Boltzmann constant (exact). https://physics.nist.gov/cgi-bin/cuu/Value?k
4. O. Maroney, “Information Processing and Thermodynamic Entropy,” Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/information-entropy/
5. A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider & E. Lutz (2012), “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187–189. https://www.nature.com/articles/nature10872
6. Y. Jun, M. Gavrilov & J. Bechhoefer (2014), “High-Precision Test of Landauer’s Principle in a Feedback Trap,” Phys. Rev. Lett. 113, 190601. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.190601
7. J. D. Norton (2005), “Eaters of the lotus: Landauer’s principle and the return of Maxwell’s demon,” Stud. Hist. Phil. Mod. Phys. 36, 375–411 (DOI 10.1016/j.shpsb.2004.12.002; metadata verified via Crossref). https://doi.org/10.1016/j.shpsb.2004.12.002
8. J. D. Norton (2011), “Waiting for Landauer,” Stud. Hist. Phil. Mod. Phys. 42, 184–198 (DOI 10.1016/j.shpsb.2011.05.002; metadata verified via Crossref). https://doi.org/10.1016/j.shpsb.2011.05.002

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.