Math 2.0

Statistical mechanics, structure of matter Fact

Landauer's principle

Builds on Second law of thermodynamicsEntropyHeatTemperature

Statement

Let a physical memory store one bit: its states form two disjoint classes, the logical states 00 and 11. Let the memory be in contact with a heat bath at absolute temperature TT, and let it hold 00 or 11 with probability 1/21/2 each. Let a physical process reset the memory to the logical state 00, whatever the initial state was. Then the mean heat QQ released into the bath satisfies Q≥kBTln⁡2,Q \ge k_B T \ln 2, where kBk_B is the Boltzmann constant.

Remarks

The idea is that the reset lowers the entropy of the memory by kBln⁡2k_B \ln 2, since two equally likely logical states become one. The second law for memory and bath together then forces the bath entropy to grow by at least kBln⁡2k_B \ln 2, that is, heat at least kBTln⁡2k_B T \ln 2 must flow into the bath. At room temperature, T=300T = 300 K, the bound is about 2.9×10−212.9 \times 10^{-21} J per bit. Logically reversible operations, which are injective on logical states, are not subject to this bound. The bound was stated by Rolf Landauer in 1961, and it was observed in experiments with a colloidal particle in a double-well potential in 2012.

Going deeper

For a student

Landauer's principle links information theory and thermodynamics: one bit of Shannon information corresponds to kBln⁡2k_B \ln 2 of thermodynamic entropy. It sets a lower bound on the energy use of irreversible computation, far below what present computers use. It is the key to the standard resolution of the paradox of Maxwell's demon, in the analysis of Charles Bennett.

Reading path

To understand this page from the ground up, read these 21 pages in order. The foundations come first.

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Entropy, concept, no evidence levelEntropyconceptHeat, concept, no evidence levelHeatconceptHeat capacity ratio, concept, no evidence levelHeat capacity ratioconceptHeat engine, concept, no evidence levelHeat engineconceptIdeal gas, concept, no evidence levelIdeal gasconceptIsentropic process, concept, no evidence levelIsentropic processconceptIsothermal process, concept, no evidence levelIsothermal processconceptReversible process, concept, no evidence levelReversible processconceptTemperature, concept, no evidence levelTemperatureconceptThermal efficiency, concept, no evidence levelThermal efficiencyconceptThermodynamic cycle, concept, no evidence levelThermodynamic cycleconceptThermodynamic system, concept, no evidence levelThermodynamic systemconceptThermodynamic temperature, concept, no evidence levelThermodynamic tempera…conceptThermodynamic work, concept, no evidence levelThermodynamic workconceptClausius statement of the second law, statement, no evidence levelClausius statement of…statementKelvin–Planck statement of the second law, statement, no evidence levelKelvin–Planck stateme…statementCarnot's theorem, statement, no evidence levelCarnot's theoremstatementCarnot cycle, example, no evidence levelCarnot cycleexampleClausius theorem, statement, no evidence levelClausius theoremstatementSecond law of thermodynamics, statement, no evidence levelSecond law of thermod…statementLandauer's principle, statement, no evidence levelLandauer's principlestatement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Entropy concept
  2. Heat concept
  3. Heat capacity ratio concept
  4. Heat engine concept
  5. Ideal gas concept
  6. Isentropic process concept
  7. Isothermal process concept
  8. Reversible process concept
  9. Temperature concept
  10. Thermal efficiency concept
  11. Thermodynamic cycle concept
  12. Thermodynamic system concept
  13. Thermodynamic temperature concept
  14. Thermodynamic work concept
  15. Clausius statement of the second law statement
  16. Kelvin–Planck statement of the second law statement
  17. Carnot's theorem statement
  18. Carnot cycle example
  19. Clausius theorem statement
  20. Second law of thermodynamics statement
  21. Landauer's principle statement

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Landauer%27s_principle
About this page
TagZPCGW6FGB0
URIm2://ZPCGW6FGB0
Kindstatement, fact
WritingW0 stub
MSC82B30, 94A17, 80A05
StatusThis copy of the site has no build data. Run m2 status ZPCGW6FGB0.
AboutEntropy
UsesSecond law of thermodynamics, Entropy, Heat, Temperature
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Changed3 November 2026

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