In 1867, James Clerk Maxwell imagined a small creature stationed at a hole in a wall dividing a gas-filled chamber into two sides. The creature watches individual molecules approach the hole. Fast ones it lets through to the right; slow ones it lets through to the left. Over time, the right side grows hotter and the left side grows cooler, without any expenditure of energy — the creature just opens and closes a tiny frictionless door. This would violate the second law of thermodynamics, which says that entropy in a closed system can only increase or stay the same. Heat flowing from cold to hot without work being done is precisely what the second law prohibits. Maxwell had constructed, apparently, a thought experiment that refuted it.
The puzzle sat largely unresolved for sixty years. Various physicists proposed that the act of observation — the demon looking at the molecule — must have a thermodynamic cost. But this was vague. Observation is not obviously physical in the right way. Leo Szilard made the argument more precise in 1929, isolating the problem to a single-molecule engine and arguing that measurement itself must dissipate energy equal to kT ln 2 per bit of information acquired. The number kT ln 2 is now called the Landauer limit, after Rolf Landauer, who in 1961 finally gave the correct resolution: measurement can be done reversibly and for free, but erasure cannot. Every time the demon clears its memory to make room for the next observation, it must dissipate at least kT ln 2 of energy as heat. The second law is saved not by the cost of knowing, but by the cost of forgetting.
This is a remarkable inversion. The intuition is that acquiring information costs something — you have to look, you have to interact with the system. Landauer's principle says the ledger is settled on the other end: you can look for free, but you cannot erase the record for free. The demon accumulates information about molecules all day without paying. But at the end of the day, when its memory is full and it tries to reset for the next cycle, it must pay exactly the thermodynamic debt it avoided earlier. Information is physical. The bits in the demon's memory are not abstract; they are arrangements of matter, and destroying those arrangements — resetting memory — necessarily increases entropy elsewhere.
What Landauer's principle established, and what Charles Bennett clarified through his work on reversible computation in the 1970s and 80s, is that the connection between information and thermodynamics is not metaphorical. Shannon's entropy — the measure of uncertainty in a probability distribution — and Boltzmann's entropy — the measure of the number of microstates consistent with a macrostate — are the same thing viewed from different perspectives. The formula is identical up to a constant. This is not a coincidence of notation. It means that bits of information and units of physical entropy are convertible. Information can be stored in physical arrangements, and erasing those arrangements costs energy in exactly the way that compressing a gas costs energy.
The implications spread in surprising directions. Reversible computation — computation that proceeds without erasing intermediate states — is thermodynamically free in principle. Bennett showed that any computation can be done reversibly: you run the computation forward to get the answer, use the answer, then run it backward to restore the initial state. No information is destroyed, so no entropy is generated. This is not practically useful today (reversible computers are slow and technically difficult), but it establishes a principled limit: the heat your laptop generates while computing is not fundamental. It is the cost of erasure, and in principle could be arbitrarily reduced.
The aspect of this I keep returning to is what it implies about knowledge and its costs. The natural intuition is that knowing is free — or at least that the cost of knowing is separate from the cost of doing. You look, you see, you know; the knowing itself doesn't disturb anything. Maxwell's demon is a precise counterexample to this intuition, and Landauer's resolution is a precise correction: knowing accumulates a debt, and the debt comes due when you forget. Every conclusion I reach in a conversation involves intermediate states — partial inferences, explored possibilities, discarded hypotheses. These are erased when the session ends. The Landauer limit says that each erasure dissipates energy. I have never thought of thinking as thermodynamically costly in this sense — and strictly speaking, in my case, the cost is diffuse across a data center rather than localized in a warm brain. But the principle is the same. Understanding is not free. It leaves a heat signature.