What is Landauer's principle about erasing information?

Landauer's principle states that the minimum energy needed to erase one bit of information is proportional to the temperature of the system. The bound is written E ≥ k_B T ln 2, where k_B is the Boltzmann constant and T is the absolute temperature. At room temperature this comes to roughly 0.018 electronvolts, or 2.9×10^-21 joules (see [en.wikipedia.org](https://en.wikipedia.org/wiki/Landauer%27s_principle)). Rolf Landauer proposed the idea in 1961, as described in [nature.com](https://www.nature.com/articles/s42254-021-00400-8). [1] [2]

Landauer's argument turns on logical irreversibility. An operation is logically irreversible if its output does not uniquely determine its inputs, as with an AND or OR gate, or with resetting a bit to a fixed value. Landauer's 1961 paper argued that this implies physical irreversibility, which is accompanied by dissipative effects ([dna.caltech.edu](https://www.dna.caltech.edu/courses/cs191/paperscs191/landauer1961.pdf)). [2] [3]

The reasoning runs through entropy. A bit that could be a 0 or a 1 has twice as many available physical states as a bit reset to a single value. Resetting a whole ensemble therefore cuts the number of states in half and lowers the entropy by k ln 2 per bit. The entropy of a closed system cannot decrease, so that entropy must appear elsewhere as heat released to the surroundings, amounting to kT ln 2 per bit. Landauer noted that this is a minimum and that his reasoning does not guarantee it can be achieved ([dna.caltech.edu](https://www.dna.caltech.edu/courses/cs191/paperscs191/landauer1961.pdf)). His 1991 essay describes the same idea as a compression of the phase space of the information-bearing degrees of freedom, which requires an expansion of other degrees of freedom ([cpt.univ-mrs.fr](https://www.cpt.univ-mrs.fr/~verga/pdfs/Landauer-1991.pdf)). [3] [4]

The principle helps explain why Maxwell's demon cannot beat the second law of thermodynamics. According to Charles Bennett's 1982 analysis, the problem is not the demon's measurement. The cost comes from erasing the demon's memory so that it can record the next measurement, because that erasure is logically irreversible ([nature.com](https://www.nature.com/articles/s42254-021-00400-8)). [2]

The bound applies to the physical system that stores the bit. Whether and how much heat is actually dissipated depends on the physical implementation, not on the logical operation alone ([en.wikipedia.org](https://en.wikipedia.org/wiki/Landauer%27s_principle)). A 2025 review also stresses that the bound concerns a single information-bearing degree of freedom within a whole computing system, and says the principle has been derived microscopically without direct reference to the second law ([pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/PMC12026021/)). [1] [5]

A 2012 experiment in Nature tested the principle directly. It used a single colloidal particle trapped in a modulated double-well potential as a one-bit memory. The mean dissipated heat approached the Landauer bound as the erasure cycles became longer ([nature.com](https://www.nature.com/articles/nature10872)). The authors had noted that the principle had not been verified experimentally before, because single-particle experiments in the low-dissipation regime are difficult. [6]