Of k_B T ln2, only the T is physics – taking the number in Landauer’s bound apart.
The third edition of Paper 04 wrote that Landauer’s bound constrains only irreversible implementations (Bennett 1973). This paper takes the number itself apart. NO NEW MATHEMATICAL THEOREM AND NO NEW PHYSICAL LAW IS CLAIMED. Landauer (1961), Bennett (1973, 1982), Szilard (1929), Brillouin (1951) and the experiment of Berut et al. (2012) are all standard.
First, the two in ln2 is a count of states, and it moves. The minimum work to collapse N equiprobable logical states into one is k_B T times ln N. The two appears only because the bit was chosen as the unit of information; in nats the coefficient is exactly one, in trits it is ln3. It is not a constant of nature. And the corpus is full of twos, but the separator is whether the number moves when something is moved. The two of ln2 moves when the number of states changes. The two of the Hopf map (Paper 68) does not: it is the structure of a fibration, not a choice of unit. The same character, a different root.
Second, the Boltzmann constant is a conversion factor. Since the 2019 SI revision it is not measured but defined, and improving measurement does not change its value; what improves is the realisation of the kelvin. Moreover, measuring temperature in energy units removes it from Landauer’s formula altogether. A quantity that a change of units removes is not physics (Papers 95, 117). And Paper 10 said that only dimensionless quantities can be tuned; k_B T ln2 carries a dimension, namely energy, so its value is not a prediction.
Third, and this is the core. What survives every choice of units is only the dimensionless content, the entropy lost in the erasure measured in nats, that is the minimum work divided by k_B T. Neither the Boltzmann constant nor ln2 occurs there. Two things remain as physics: that the bound is proportional to temperature, and that it is not zero. Paper 129 said that hbar is not on the mathematical side of the inequality; here the census runs the other way. In Landauer’s bound it is the number that is mostly convention, and the physics resides only in two statements, a proportionality and a non-vanishing. And those two are not light. That erasing information carries a thermodynamic price is itself a discovery, and it has been verified experimentally (Berut et al. 2012). Strip the conventions and what remains, remains.
Fourth, an irreversible gate does not pay one bit. It is sometimes said that an irreversible logic gate dissipates k_B T ln2 per operation. This is not correct. For an AND gate with two independent inputs, each Bernoulli with parameter p, this paper computes the logical entropies of input and output. For uniform inputs the input carries 2.0000 bits and the output 0.8113 bits, so the reduction is 1.1887 bits, not one. And it moves with the input distribution: 1.3261 at p equal to 0.3, 0.8572 at 0.1, and 0.2365 at 0.9, ranging both above one and below it. What sets the cost is neither the number of wires nor the number of gates but the reduction of logical entropy. The phrase ‘a one-bit gate’ names two different quantities with one word, the width of the output and the information lost, and they agree only in special cases.
Fifth, the same number has historically been placed at two different steps. Szilard (1929) and Brillouin put it at measurement; Landauer (1961) and Bennett (1982) put it at erasure. Both assign the same number to different steps of the same cycle: the number is the same and the address is different. And the second replaced the first, because measurement into a blank memory can be built reversibly, whereas memory is finite and closing the cycle requires resetting it. That is where the price falls due. Here is the lesson for the corpus. That a number explains something successfully does not establish where it was placed. Brillouin’s assignment was numerically right; what was wrong was the address (Paper 17). An agreement of numbers is not a proof of address (Paper 100).
Sixth, the bound is a boundary never reached. In the standard finite-time form the work of erasure is the bound plus a term inversely proportional to the duration. This paper confirms that the limit of infinite duration is the bound and that the excess is positive for every finite duration. Landauer’s bound is a statement about work and says nothing about time. The phrase ‘the minimum energy’ is doubly inaccurate: it is work, not energy, and it is not attained in finite time. Paper 113 drew the distinction between a wall and a slope, and Landauer’s bound is the foot of a slope, not a wall.
IMPORTANT (scope): a census of established standard material (Layer 2). Every work cited is standard. What is not claimed: any new mathematical theorem (there is none) / any new physical law (there is none) / that Landauer’s bound is wrong (it is not, and it has been verified experimentally) / that the link between information and thermodynamics is a mere convention (it is not; what is conventional is how the number is written, while the link itself is a fact). What is added: sorting k_B T ln2 into convention, convention and fact; computing the cost of an irreversible gate and showing it is not one bit; setting the two addresses of one number side by side; and making explicit that the bound is a boundary never reached. What remains: the ln2 is the trace of our having chosen the bit, and the Boltzmann constant the trace of our having chosen the kelvin. What nature chose is the single fact that erasure has a price. And that alone is large enough.
On the making of this work: The ideas and content of this work stem from the author’s own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author’s. Feedback and corrections are sincerely appreciated.
Reference
Yamagishi, Y. (2026). Of $k_BT\ln2$, Only the $T$ Is Physics [Paper 131]. Zenodo.
DOI: 10.5281/zenodo.22080240
ORCID: 0009-0006-8587-3450