In 1867 Maxwell imagined a tiny being who watches gas molecules and opens a trapdoor only for fast ones — sorting hot from cold for free, apparently breaking the second law of thermodynamics. The resolution took a century: the demon must remember what it sees, and erasing that memory costs exactly the entropy it seemed to save. Information is physical.
why information has a thermodynamic price
The setup: a box of gas at uniform temperature, split by a wall with a trapdoor. The demon opens the door to let fast molecules go right and slow ones go left. After a while the right side is hot, the left cold — a temperature difference built from nothing, which you could run a heat engine on. The gas entropy decreases. The second law appears violated.
Szilard (1929) reframed it: each decision the demon makes requires measuring which side a molecule is on — acquiring 1 bit of information. The demon's brain (or notebook) fills up with bits as it sorts.
Landauer's principle (1961) is the resolution: erasing one bit of information in a system at temperature T necessarily dissipates at least k_B T ln 2 of heat into the environment — about 3 × 10⁻²¹ joules at room temperature. Logically irreversible operations have an unavoidable thermodynamic cost. The demon can sort for free, but to keep going it must eventually reset its finite memory, and that erasure dumps exactly enough entropy to balance the books.
ΔS_universe = ΔS_gas + ΔS_erasure ≥ 0
The ledger above tracks both columns: the gas entropy falls as sorting proceeds, but the demon's accumulated bits, when erased, cost k ln2 each — always paying back the deficit. The second law survives because information is physical.
Bennett (1982) sharpened this: the measurement and the sorting can in principle be done reversibly (no cost). The only unavoidable cost is in forgetting — resetting the memory to a blank state. This is the deep link between computation and thermodynamics.
Confirmed in the lab: in 2012 Bérut et al. measured the Landauer bound directly with a single colloidal particle in an optical trap, watching erasure dissipate the predicted k_B T ln 2. It sets the ultimate energy floor for all computing — today's chips run ~10,000× above the Landauer limit, but it is the wall that irreversible computation can never cross. (Reversible computing aims to dodge it entirely.)