The Landauer Gap
How far a computation is from the physical minimum energy for erasing information. Lower is better; it cannot go below 1 for irreversible logic.
The bound
Emin = kB · T · ln 2
Rolf Landauer showed that erasing one bit of information costs at least this much energy (Landauer, 1961). With the exact Boltzmann constant, kB = 1.380649 × 10−23 J/K, at 300 K the bound is about 2.87 × 10−21 J per bit.
The ratio
LG = Eper erasure / (kB · T · ln 2)
The denominator uses the declared count of irreversible bit erasures, and the counting method must be stated. Device temperature is measured; using a 300 K fallback makes the result Estimated.
The evidence
Experiments have confirmed the bound: with a colloidal particle in a laser trap (Bérut et al., 2012), and in nanomagnetic memory bits, measured at 4.2 ± 0.9 zJ per erased bit (Hong et al., 2016). Current hardware sits many orders of magnitude above the bound, roughly 104 to 108 times depending on what counts as one operation (Ho et al., 2023).
Assumptions, stated
- Only logically irreversible operations count; reversible computing can in principle go below the bound per operation.
- Counting erasures in real hardware is a modeling choice and must be declared.
- The ratio is "not applicable" to living-neuron cultures.
- Critiques are welcome through the contact page; substantive ones are listed in the changelog.
Questions
Is the Landauer Gap useful for operators?
Mostly for hardware designers and researchers. Operators usually get more from Decision Yield and the Overhead Ratio.
Sources
Keep reading
Take the next step.
The Landauer Gap compares the energy per irreversible bit operation with the physical minimum, k_B·T·ln 2: the derivation, units, assumptions and evidence.