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Landauer's principle relates logically irreversible information erasure to thermodynamic cost. Resetting an initially equiprobable, uncorrelated one-bit memory to one standard state while coupled to a bath at temperature $T$ requires average heat release of at least $k_{B}T\ln 2$ to the bath in the ideal cyclic setting.

The restriction matters: erasing one unknown bit is different from reversibly transforming a known state, and real devices can dissipate more. The entropy reduction of the memory must be compensated elsewhere. The bound therefore concerns information loss under specified physical conditions, rather than a universal cost for every logic operation.^[ref]

A later experiment represented a bit by the two wells of a potential trapping one colloidal particle. Driving the particle distribution into a chosen well allowed dissipated heat during erasure to be compared with the bound. Approaching the reversible limit requires slow controlled operations; measurement of the work and heat connects the information statement to a physical apparatus.^[ref]

Maxwell's demon is a thought experiment in which a controller measures microscopic motion and selectively operates a barrier, apparently driving a system away from thermal equilibrium without the usual thermodynamic cost. For example, admitting fast gas particles preferentially to one side seems to create a temperature difference that a heat engine could exploit.

The controller must be included in the physical accounting. Its measurement record becomes correlated with the gas, and a repeatable cyclic device must deal with that record rather than treating information storage as an unlimited free resource. Landauer's principle connects logically irreversible memory erasure with a thermodynamic cost under its stated conditions. This does not mean that every measurement automatically dissipates exactly one bit's erasure cost. The point is to track the complete cycle, correlations and resources. A controller that reduces one subsystem's entropy can still respect the Second law of thermodynamics by increasing entropy elsewhere.

Rolf Landauer connected logical irreversibility with physical entropy production. His 1961 analysis examined operations whose outputs do not uniquely determine their inputs, making the discarded information part of the thermodynamic accounting.^[ref]

For the ideal isothermal erasure of an initially unbiased bit into one standard state, Landauer's principle gives a minimum reservoir heat $Q\ge k_{B}T\ln 2$ under the usual cyclic-device assumptions. The information-bearing system loses entropy, which must be accounted for elsewhere. This statement concerns the specified erasure process; it is not a universal fixed heat cost for every reversible logical operation.