Math 2.0

Classical thermodynamics, heat transfer Non-equilibrium thermodynamics Problem

Maxwell's demon

Builds on Second law of thermodynamicsEntropyLandauer's principle

Problem

A gas at uniform temperature fills a box split into two halves by a wall with a small door. A being, the demon, watches the molecules and works the door. It lets fast molecules pass only from left to right, and slow molecules only from right to left. It seems to make the right half hotter and the left half colder without doing work. This would lower the entropy of the isolated gas. The problem is to explain why this does not violate the second law of thermodynamics.

Remarks

Leo Szilard in 1929 reduced the problem to a one-molecule engine and argued that measurement by the demon must produce entropy. The standard resolution today, due to Charles Bennett in 1982, uses Landauer's principle: measurement can in principle be done reversibly, but the demon must store its results. To work in a cycle, it must erase its memory. The erasure releases at least kBTln⁡2k_B T \ln 2 of heat per bit, which makes up for the entropy decrease of the gas. The name "demon" was given by William Thomson, later Lord Kelvin. Some authors still question parts of this resolution, but within statistical mechanics the second law is regarded as safe.

Reading path

To understand this page from the ground up, read these 22 pages in order. The foundations come first.

Show the path as a graph
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 principlestatementMaxwell's demon, problem, no evidence levelMaxwell's demonproblem
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
  22. Maxwell's demon problem

Further reading

  1. Web https://en.wikipedia.org/wiki/Maxwell%27s_demon
About this page
TagHABM6R27XZ
URIm2://HABM6R27XZ
Kindproblem
WritingW0 stub
MSC80A05, 82B30, 94A17
StatusThis copy of the site has no build data. Run m2 status HABM6R27XZ.
AboutSecond law of thermodynamics
UsesSecond law of thermodynamics, Entropy, Landauer's principle
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Changed3 November 2026

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