The statement
In 1961 Rolf Landauer, a physicist at IBM, asked what the minimum energy cost of computation is (IBM Journal of Research and Development 5, 183). His answer: most operations can in principle be done without any cost, but erasing information cannot.
Erasing one bit, resetting a memory cell to 0 regardless of whether it held 0 or 1, must release at least
E = kT ln 2
of heat into the environment, where k is Boltzmann's constant and T is the temperature. At room temperature (300 K) that is about 2.9 × 10⁻²¹ J, roughly 0.018 electron-volts.
Why erasure has a cost
A memory that can hold 0 or 1 has two possible states. After erasure it has one. The number of possible states of the memory has halved, so its entropy has dropped by k ln 2. The second law of thermodynamics does not allow total entropy to fall, so at least that much entropy has to go somewhere else, as heat into the surroundings.
The key step is that the bit is a physical state of a physical system. Landauer summed it up in a phrase that became a slogan: information is physical.
Maxwell's demon, resolved
In 1867 James Clerk Maxwell imagined a tiny being that opens a door between two gas chambers to let fast molecules one way and slow ones the other. It would create a temperature difference, apparently for free, against the second law.
Charles Bennett showed in 1982 where the cost hides. To sort molecules the demon has to record what it saw. To keep working it must eventually erase those records, and by Landauer's principle the erasure dissipates at least as much entropy as the sorting removed. The second law survives because memory is physical.
The measurement
For fifty years the principle was a theoretical result. In 2012 Antoine Bérut and colleagues tested it directly (Nature 483, 187). They trapped a single glass bead in a double-well potential made by lasers, where "left" and "right" served as 0 and 1, and performed erasure cycles while measuring the heat. As the cycles were run more slowly, the released heat approached kT ln 2 and did not go below it. Experiments with nanomagnetic bits (Hong et al., Science Advances, 2016) and quantum systems followed.
What it means for computers
Today's chips dissipate many orders of magnitude more energy per operation than the Landauer limit. The limit matters for the future: it sets a floor for irreversible computing and motivates reversible computing, where logic is designed so that no information is erased and the floor can, in principle, be avoided.
Why it matters for physics built on information
Landauer's principle is the best-established link between information and energy. It is one of the foundations for ideas that treat information as a primary physical quantity: Wheeler's "it from bit", Bekenstein's entropy of black holes, Verlinde's emergent gravity.
The research programme on this site builds the same link into its substrate. In the Pointer Architecture preprint, history is kept in an append-only archive that is never erased, and the paper proves that this archive can be compressed at the Shannon rate. In Landauer's terms, the substrate never pays the cost of erasure, because nothing is erased; its records are compressed instead.
Bottom line
Erasing a bit costs at least kT ln 2 of heat. The principle is experimentally confirmed, it resolved Maxwell's demon and it makes "information is physical" a measurable statement.