Use of mutual information to decrease entropy: Implications for the second law of thermodynamics

Phys. Rev. A 39, 5378 – Published 15 May 1989
Seth Lloyd


Several theorems on the mechanics of gathering information are proved, and the possibility of violating the second law of thermodynamics by obtaining information is discussed in light of these theorems. Maxwell’s demon can lower the entropy of his surroundings by an amount equal to the difference between the maximum entropy of his recording device and its initial entropy, without generating a compensating entropy increase. A demon with human-scale recording devices can reduce the entropy of a gas by a negligible amount only, but the proof of the demon’s impracticability leaves open the possibility that systems highly correlated with their environment can reduce the environment’s entropy by a substantial amount without increasing entropy elsewhere. In the event that a boundary condition for the universe requires it to be in a state of low entropy when small, the correlations induced between different particle modes during the expansion phase allow the modes to behave like Maxwell’s demons during the contracting phase, reducing the entropy of the universe to a low value.


  • Received 5 December 1988
  • Published in the issue dated May 1989

© 1989 The American Physical Society

Authors & Affiliations

Seth Lloyd

  • The Rockefeller University, 1230 York Avenue, New York, New York 10021

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