Next Article in Journal
Factorization and Criticality in the Anisotropic XY Chain via Correlations
Previous Article in Journal
Fokker-Planck Equation and Thermodynamic System Analysis
Article Menu

Export Article

Open AccessArticle
Entropy 2015, 17(2), 772-789; doi:10.3390/e17020772

Quantropy

1
Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
2
Department of Mathematics, University of California, Riverside, CA 92521, USA
3
Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
*
Author to whom correspondence should be addressed.
Received: 17 December 2014 / Accepted: 30 January 2015 / Published: 9 February 2015
(This article belongs to the Section Quantum Information)
View Full-Text   |   Download PDF [225 KB, uploaded 24 February 2015]   |  

Abstract

There is a well-known analogy between statistical and quantum mechanics. In statistical mechanics, Boltzmann realized that the probability for a system in thermal equilibrium to occupy a given state is proportional to \(\exp(-E/kT)\), where \(E\) is the energy of that state. In quantum mechanics, Feynman realized that the amplitude for a system to undergo a given history is proportional to \(\exp(-S/i\hbar)\), where \(S\) is the action of that history. In statistical mechanics, we can recover Boltzmann's formula by maximizing entropy subject to a constraint on the expected energy. This raises the question: what is the quantum mechanical analogue of entropy? We give a formula for this quantity, which we call ``quantropy''. We recover Feynman's formula from assuming that histories have complex amplitudes, that these amplitudes sum to one and that the amplitudes give a stationary point of quantropy subject to a constraint on the expected action. Alternatively, we can assume the amplitudes sum to one and that they give a stationary point of a quantity that we call ``free action'', which is analogous to free energy in statistical mechanics. We compute the quantropy, expected action and free action for a free particle and draw some conclusions from the results. View Full-Text
Keywords: path integration; variational principles; quantum mechanics; entropy path integration; variational principles; quantum mechanics; entropy
Figures

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Baez, J.C.; Pollard, B.S. Quantropy. Entropy 2015, 17, 772-789.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top