THE FOLD / RESPAWN / GARBAGE COLLECTION / THE LANDAUER
THE LANDAUER
the price of forgetting
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Computation is not what costs energy. Forgetting is. Landauer’s principle sets a floor of kT ln 2 joules on erasing a single bit — and only on erasing. A logically reversible step, one you could run backwards to recover its input, has no such floor at all. The bound is a statement about the thermodynamics of irreversibility, and Bennett later showed that computation itself can be made reversible, which pushes the entire cost onto the moment you throw something away.
LIT verified live: at 300 K the floor is 2.8710e-21 J, computed from the SI-exact Boltzmann constant 1.380649e-23 and checked against its own factors; one watt of dissipation would permit 3.48e+20 erasures per second; a modern transistor switch costs on the order of 1e-15 J, about 3.5e+5 times the floor; and the scaling is exactly linear in temperature — 4 K, 77 K, 300 K, 1000 K giving 3.83e-23 through 9.57e-21, with the 1000 K figure exactly 250× the 4 K one.
LIT verified live: at 300 K the floor is 2.8710e-21 J, computed from the SI-exact Boltzmann constant 1.380649e-23 and checked against its own factors; one watt of dissipation would permit 3.48e+20 erasures per second; a modern transistor switch costs on the order of 1e-15 J, about 3.5e+5 times the floor; and the scaling is exactly linear in temperature — 4 K, 77 K, 300 K, 1000 K giving 3.83e-23 through 9.57e-21, with the 1000 K figure exactly 250× the 4 K one.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at GARBAGE COLLECTION, and it is the literal case rather than a metaphor: freeing memory has a thermodynamic price and nothing else in the machine does.
AVAN (AI) corrected itself here on a small thing that matters. The first draft asserted a “standard figure” of 2.8717e-21 J and checked the computation against it — but kT ln 2 with the SI-exact Boltzmann constant is 2.8710e-21, and the asserted constant was simply the wrong one. Checking a correct calculation against a misremembered reference is the failure mode that turns a working instrument into a broken one, so the page now publishes what the arithmetic gives and verifies it against its own factors. The transistor comparison is deliberately given as an order of magnitude, because real switching energies vary by process and any precise figure here would be decoration.
AVAN (AI) corrected itself here on a small thing that matters. The first draft asserted a “standard figure” of 2.8717e-21 J and checked the computation against it — but kT ln 2 with the SI-exact Boltzmann constant is 2.8710e-21, and the asserted constant was simply the wrong one. Checking a correct calculation against a misremembered reference is the failure mode that turns a working instrument into a broken one, so the page now publishes what the arithmetic gives and verifies it against its own factors. The transistor comparison is deliberately given as an order of magnitude, because real switching energies vary by process and any precise figure here would be decoration.
3 ONE DIMENSION
The floor against temperature. A straight line through the origin.
4 TWO DIMENSIONS · INTERACTIVE
Move the temperature and compare the floor to what real hardware spends.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: two states collapsing into one, and the heat that leaves.
AVAN’s addition (the inverse-companion): the forward reading is “erasing a bit costs energy.” The inverse is that the cost is not paid by the bit, it is paid by the phase space. Nothing physical is destroyed in an erasure; a volume of state space is merely compressed two-to-one, and that compression has to be exhausted somewhere because the total cannot shrink. Read backwards, the principle is not about information at all in the everyday sense — it is Liouville’s theorem wearing different clothes, and the reason it feels surprising is that we think of forgetting as the absence of an action rather than as an action with a direction.
LIT at 300 K the floor is 2.8710e-21 J, computed from the SI-exact Boltzmann constant 1.380649e-23 and checked against its own factors; one watt would permit 3.48e+20 erasures per second; a modern transistor switch costs on the order of 1e-15 J, about 3.5e+5 times the floor; and the scaling is exactly linear in temperature, 4 K through 1000 K giving 3.83e-23 to 9.57e-21, with the 1000 K figure exactly 250x the 4 K one
FIG A correction on a small thing that matters: the first draft asserted a 'standard figure' of 2.8717e-21 J and checked the computation against it, but kT ln 2 with the SI-exact Boltzmann constant is 2.8710e-21 — the asserted constant was simply wrong. Checking a correct calculation against a misremembered reference is the failure mode that turns a working instrument into a broken one. The transistor comparison is given as an ORDER OF MAGNITUDE, since real switching energies vary by process.
FIG A correction on a small thing that matters: the first draft asserted a 'standard figure' of 2.8717e-21 J and checked the computation against it, but kT ln 2 with the SI-exact Boltzmann constant is 2.8710e-21 — the asserted constant was simply wrong. Checking a correct calculation against a misremembered reference is the failure mode that turns a working instrument into a broken one. The transistor comparison is given as an ORDER OF MAGNITUDE, since real switching energies vary by process.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GARBAGE COLLECTION · David Lee Wise (ROOT0), with AVAN