Maxwell's Demon and Landauer's Principle

Why Erasing One Bit of Memory Must Dump Heat Into the Room

A microscopic gatekeeper sits beside a frictionless sliding shutter in the wall dividing an insulated gas chamber into two equal compartments, $A$ and $B$. Both compartments start at the exact same temperature, meaning their gas molecules share the same average kinetic speed. Yet as James Clerk Maxwell pointed out in a December 1867 letter to fellow Scottish physicist Peter Guthrie Tait, individual molecules travel at widely different velocities around that average. Whenever the gatekeeper spots a faster-than-average molecule hurtling from $A$ toward $B$, it opens the massless shutter to let the molecule pass. Whenever a slower-than-average molecule approaches from $B$ toward $A$, it lets that slow molecule cross the other way.

Without expending mechanical work or applying an external flame, the creature—dubbed Maxwell's demon by William Thomson in 1874—gradually packs fast molecules into chamber $B$ and slow molecules into chamber $A$. One side grows hot while the other grows cold. A steam engine connected between the two halves could now extract work from a single heat bath, violating the second law of thermodynamics. For ninety-four years, physicists tried to exorcise the demon by arguing that shining a light photon to measure a molecule's speed must scatter energy and create compensating entropy.

In 1929, Hungarian physicist Leo Szilard simplified the puzzle at the University of Berlin. He stripped the gas down to a single molecule bouncing inside a cylinder fitted with a central partition and two frictionless pistons. Whenever the demon detects whether the lone molecule sits on the left or right side of the partition, it inserts a piston and lets the gas expand isothermally at temperature $T$. That expansion extracts $W = k_B T \ln 2$ of mechanical work. Szilard realized that the demon must record that binary left-or-right choice in a physical memory register. One bit of recorded information therefore links directly to $k_B \ln 2$ of thermodynamic entropy.

The true physical ledger remained blurry until 1961. At the IBM Thomas J. Watson Research Center in Yorktown Heights, New York, German-born physicist Rolf Landauer analyzed the thermodynamics of computer hardware. Landauer proved that logical operations preserving a one-to-one mapping between inputs and outputs can, in principle, run with zero energy dissipation. By contrast, any logically irreversible operation—such as a CLEAR or RESET instruction that maps both a 0 and a 1 onto the single standard state 0—compresses the physical phase space of the memory device by a factor of two. Liouville's theorem forbids phase-space volume from vanishing in a closed Hamiltonian system. Therefore, that two-to-one compression inside the memory bit must expel an equal factor of phase-space spread into the thermal vibrations of the surrounding hardware. Erasing one bit must dissipate at least $E_{\min} = k_B T \ln 2$ of heat.

In 1982, Landauer's IBM colleague Charles Bennett completed the exorcism of Maxwell's demon. Bennett demonstrated that a demon can measure a molecule's position reversibly with zero thermodynamic cost by coupling the molecule to a bistable magnetic or mechanical switch. The demon's bill comes due only at the end of the cycle, when its finite notebook fills up and it must erase old bits to make room for new observations. That erasure dumps the exact $k_B T \ln 2$ of heat back into the bath that the demon harvested during expansion. In 2012, physicist Antoine Bérut and his colleagues at the École Normale Supérieure de Lyon trapped a two-micrometer silica bead inside a double-well laser potential in water. When they forced the bead from either well into a single target state, erasing one bit of position memory dissipated the exact Landauer limit of $2.87 \times 10^{-21}$ joules at room temperature.