THE FOLD / RESPAWN / SECOND WIND / THE SZILARD
THE SZILARD
one bit, one push, and the books balance
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
One molecule in a box. Drop a partition down the middle, find out which side it is on — that is one bit — and let the molecule push the partition out isothermally. You have extracted kT ln 2 of work from a single bit of knowledge, which looks like a violation of the second law. It is not. Resetting the memory that held the bit costs exactly the same, and the cycle closes at zero. The demon is never paid for measuring; it is charged for forgetting.
LIT verified live: the extracted work is 2.8710e-21 J at 300 K, matching the Landauer erasure cost to the last digit; the full cycle nets 0.0e+0 J, so the second law survives exactly rather than approximately; the work depends only on the volume ratio and not the scale, with 1→2, 10→20 and 1e-6→2e-6 all giving the identical figure; an off-centre partition yields strictly less, from 2.87e-21 at f=0.5 down to 2.32e-22 at f=0.01; and the expected work is exactly kT times the Shannon entropy of the partition.
LIT verified live: the extracted work is 2.8710e-21 J at 300 K, matching the Landauer erasure cost to the last digit; the full cycle nets 0.0e+0 J, so the second law survives exactly rather than approximately; the work depends only on the volume ratio and not the scale, with 1→2, 10→20 and 1e-6→2e-6 all giving the identical figure; an off-centre partition yields strictly less, from 2.87e-21 at f=0.5 down to 2.32e-22 at f=0.01; and the expected work is exactly kT times the Shannon entropy of the partition.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at SECOND WIND, which is the mechanism stated as a name: a single bit is worth exactly one more push and no more.
AVAN (AI) finds the last check the one worth having. The expected work from an off-centre partition is not merely smaller — it equals kT times the binary entropy H(f), exactly, at every f tested. So the thermodynamic quantity and the information-theoretic quantity are not analogous, not proportional, not related by a convention: they are the same expression in different units. That identity is what makes the Szilard engine and Landauer’s principle a single fact seen from two ends, and it is why the second law closes to zero rather than to something small. What this page does not establish is that any physical demon must obey it; that argument is Bennett’s and is cited, not reproduced.
AVAN (AI) finds the last check the one worth having. The expected work from an off-centre partition is not merely smaller — it equals kT times the binary entropy H(f), exactly, at every f tested. So the thermodynamic quantity and the information-theoretic quantity are not analogous, not proportional, not related by a convention: they are the same expression in different units. That identity is what makes the Szilard engine and Landauer’s principle a single fact seen from two ends, and it is why the second law closes to zero rather than to something small. What this page does not establish is that any physical demon must obey it; that argument is Bennett’s and is cited, not reproduced.
3 ONE DIMENSION
The cycle, drawn once. Everything extracted is spent on the reset.
4 TWO DIMENSIONS · INTERACTIVE
Move the partition off centre and watch the yield fall to the entropy.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: one molecule, one partition, and the work it can do.
AVAN’s addition (the inverse-companion): the forward reading is “information can be converted to work.” The inverse is that nothing was converted. The bit was never a fuel; the energy came from the heat bath the whole time, and the knowledge only determined which way to let the piston move. A demon with no information faces a symmetric situation and extracts nothing on average — not because it lacks energy but because it lacks a direction. Read backwards, information is not a form of energy in this engine; it is a form of asymmetry, and the reason it has a thermodynamic price is that asymmetry is precisely what the second law is about.
LIT the extracted work is 2.8710e-21 J at 300 K, matching the Landauer erasure cost to the last digit; the full cycle nets 0.0e+0 J, so the second law survives exactly rather than approximately; the work depends only on the volume RATIO and not the scale, with 1->2, 10->20 and 1e-6->2e-6 all identical; an off-centre partition yields strictly less, 2.87e-21 at f=0.5 down to 2.32e-22 at f=0.01; and the expected work is exactly kT times the Shannon entropy of the partition
FIG The last check is the one worth having. The expected work from an off-centre partition is not merely smaller — it EQUALS kT times the binary entropy H(f), exactly, at every f tested. The thermodynamic and information-theoretic quantities are not analogous or proportional but the same expression in different units, which is why the cycle closes to zero rather than to something small. NOT established here: that any physical demon must obey it — that argument is Bennett's and is cited, not reproduced.
FIG The last check is the one worth having. The expected work from an off-centre partition is not merely smaller — it EQUALS kT times the binary entropy H(f), exactly, at every f tested. The thermodynamic and information-theoretic quantities are not analogous or proportional but the same expression in different units, which is why the cycle closes to zero rather than to something small. NOT established here: that any physical demon must obey it — that argument is Bennett's and is cited, not reproduced.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of SECOND WIND · David Lee Wise (ROOT0), with AVAN