To me, every statistical ensemble in statistical physics was introduced beginning with the microcanonical ensemble, in which every microstate is equally probable. A canonical ensemble is described by combining two ensembles, who together shall form a microcanonical ensemble. The microstates in system 1 shall then form the canonical ensemble, system 2 is said to be large compared to system 1, so that it's temperature $T = \frac{\partial S}{\partial E}$ doesn't change when the two systems interchange energy. If one still requires every possible microstate of the whole system to be equally probable, then the probabilities for microstates $\Gamma$ in the small system scale with a factor $e^{-\frac{H(\Gamma)}{k_b T}}$. The canonical ensemble is no longer described by its energy, but by its temperature ( and volume V, particle number N ....)

My question: Is there also a way to describe an ensemble that has a fixed Energy, E, but varying Volume, that means, a EpN Ensemble, or a SpN Ensemble? That would mean that I look at two systems that can interchange Volume, but don't interchange energy, in the same way I described it above for the canonical ensemble.

I am asking because the Enthalpie H(S,p,N) exists, and is a thermodynamical potential that depends on S,p,N, which suggests that such an ensemble exists.

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    $\begingroup$ Implementation: An insulated system with a piston that ensures constant pressure (i.e. with a weight on top). $\endgroup$ Jan 2, 2016 at 22:06
  • $\begingroup$ @SebastianRiese: That's the answer, isn't it? $\endgroup$
    – CuriousOne
    Jan 3, 2016 at 3:24
  • $\begingroup$ wouldn't the two systems interchange energy anytime they would interchange volume? $\endgroup$ Jan 3, 2016 at 11:27
  • $\begingroup$ Well, technically, it is an $S, p, N$ ensemble, not an $E, p, N$ ensemble, and the entropy remains constant (in both systems). $E$ can't be a natural variable of a thermodynamic ensemble. $\endgroup$ Jan 3, 2016 at 14:42
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    $\begingroup$ Connecting two vessels with a movable wall is called 'the adiabatic piston problem' which somehow is still somewhat controversial physics.stackexchange.com/questions/257815/… $\endgroup$
    – lalala
    Jul 30, 2017 at 15:54

1 Answer 1


Yes. It is called the Isoenthalpic-isobaric Ensemble. See my answer for more details, but remember that moving between different ensembles is as simple as a Laplace transform or a Legendre transform (that answer will show more details). So you can really construct as many "ensembles" as you have Thermodynamic variables to do so.

  • $\begingroup$ "Moving between different ensembles is as simple as a Laplace transform or Legendre transform". This is only true for the thermodynamic limit. $\endgroup$ Aug 2, 2017 at 5:43
  • $\begingroup$ Are you asking about systems of few particles? $\endgroup$
    – user92177
    Aug 2, 2017 at 12:49

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