Skip to main content

Justification of the Maximum Entropy Criterion in Quantum Mechanics

  • Chapter
Maximum Entropy and Bayesian Methods

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 36))

  • 901 Accesses

Abstract

By relying on the principle of indifference in a form suited to quantum mechanics, we prove that the density operator which should be assigned to a quantum system when only partial information is available has a generalized canonical form. This result provides an indirect justification of the quantal maximum entropy criterion, based on the use of von Neumann’s entropy with constraints on the known expectation values.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. E.T. Jaynes, IEEE Trans. Syst. Sci. Cybernetics 4 (1968) 227;

    Article  MATH  Google Scholar 

  2. J.E. Shore and R.W. Johnson, IEEE Trans. Inf. Theory 26 (1980) 26;

    Article  MathSciNet  MATH  Google Scholar 

  3. J.E. Shore and R.W. Johnson, IEEE Trans. Inf. Theory 27 (1981) 472;

    Article  MathSciNet  MATH  Google Scholar 

  4. J.E. Shore and R.W. Johnson, IEEE Trans. Inf. Theory 29 (1983) 942;

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Thirring, “Quantum Mechanics of Large Systems”, p.59 (Springer-Verlag, New York, 1983);

    MATH  Google Scholar 

  6. Y. Tikochinsky, N.Z. Tishby and R.D. Levine, Phys. Rev. Lett. 52 (1984) 1357;

    Article  Google Scholar 

  7. Y. Tikochinsky, N.Z. Tishby and R.D. Levine, Phys. Rev. Lett. 55 (1985) 336;

    Article  Google Scholar 

  8. Y. Tikochinsky, N.Z. Tishby and R.D. Levine, Phys. Rev. A 30 (1984) 2638: Proof of the Maximum Entropy Principle in classical statistics.

    Article  Google Scholar 

  9. R. Balian and N.L. Balazs, Ann. Phys. 179 (1987) 97: Proof of the Maximum Entropy Principle in quantum mechanics.

    Article  MathSciNet  Google Scholar 

  10. R. Balian, Y. Alhassid and H. Reinhardt, Phys. Rep. 131 (1986) 1: Relevant entropy relative to a set of observables; use of — d2 S as a metric in the space of (quantum) states; applications to irreversible statistical mechanics.

    Article  MathSciNet  Google Scholar 

  11. R. Balian, M. Vénéroni and N.L. Balazs, Europhys. Lett. 1 (1986) 1: Importance of the underlying invariant measure in the definition of entropies.

    Article  Google Scholar 

  12. R. Balian and M. Vénéroni, Ann. Phys. 174 (1987) 229; R. Balian, subm. to Am. J. Phys.; subm. to Europ. J. Phys. : Incomplete preparations and measurements in quantum mechanics; projection of the state; entropy changes in a measurement.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Balian, R. (1989). Justification of the Maximum Entropy Criterion in Quantum Mechanics. In: Skilling, J. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7860-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-7860-8_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4044-2

  • Online ISBN: 978-94-015-7860-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics