Summary of Equilibrium Statistical Ensembles

  • Andrés Santos
Part of the Lecture Notes in Physics book series (LNP, volume 923)


In this chapter a summary of the main equilibrium ensembles is presented, essentially to fix part of the notation that will be needed later on. The phase-space probability density associated with each ensemble is derived by maximization of the Gibbs entropy under the appropriate constraints. For simplicity, most of this chapter is restricted to one-component systems, although the extension to mixtures is straightforward and is presented in the last section.


Partition Function Thermodynamic Limit Canonical Ensemble Thermodynamic Potential Isothermal Compressibility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    H. Goldstein, J. Safko, C.P. Poole, Classical Mechanics (Pearson Education, Upper Saddle River, 2013)zbMATHGoogle Scholar
  2. 2.
    R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1974)zbMATHGoogle Scholar
  3. 3.
    L.E. Reichl, A Modern Course in Statistical Physics, 1st edn. (University of Texas Press, Austin, 1980)zbMATHGoogle Scholar
  4. 4.
    F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, Boston, 1965)Google Scholar
  5. 5.
    C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1971)zbMATHGoogle Scholar
  6. 6.
    A. Ben-Naim, A Farewell to Entropy: Statistical Thermodynamics Based on Information (World Scientific, Singapore, 2008)CrossRefzbMATHGoogle Scholar
  7. 7.
    M. Baus, C.F. Tejero, Equilibrium Statistical Physics. Phases of Matter and Phase Transitions (Springer, Berlin, 2008)Google Scholar
  8. 8.
    R. Kubo, Statistical Mechanics. An Advanced Course with Problems and Solutions (Elsevier, Amsterdam, 1965)Google Scholar
  9. 9.
    L.D. Carr, Science 339, 42 (2013)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    S. Braun, J.P. Ronzheimer, M. Schreiber, S.S. Hodgman, T. Rom, I. Bloch, U. Schneider, Science 339, 52 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    V. Romero-Rochín, Phys. Rev. E 88, 022144 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    J. Dunkel, S. Hilbert, Nat. Phys. 10, 67 (2014)CrossRefGoogle Scholar
  13. 13.
    S. Hilbert, P. Hänggi, J. Dunkel, Phys. Rev. E 90, 062116 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    J.M.G. Vilar, J.M. Rubi, J. Chem. Phys. 140, 201101 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    D. Frenkel, P.B. Warren, Am. J. Phys. 83, 163 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    L. Ferrari, Boltzmann vs Gibbs: a finite-size match (2015), Google Scholar
  17. 17.
    P. Hänggi, S. Hilbert, J. Dunkel, Philos. Trans. R. Soc. A 374, 20150039 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Andrés Santos
    • 1
  1. 1.Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx)Universidad de ExtremaduraBadajozSpain

Personalised recommendations