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I have a question about the variables in thermodynamics. In the ensembles there are three natural variables, that are constant.

  1. Is it possible that more than these 3 are constant?

  2. What does this mean?

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  • $\begingroup$ I didn't understand what you meant. $\endgroup$
    – Karthik
    Feb 15, 2019 at 15:44
  • $\begingroup$ Can you be more specific? $\endgroup$ Feb 15, 2019 at 15:47
  • $\begingroup$ Yes, so for example if I have a microcanonical ensemble than N, V, E are constants of the ensembles, as Wiki explains it $\endgroup$
    – Q.stion
    Feb 18, 2019 at 16:11
  • $\begingroup$ The macroscopic variables of the microcanonical ensemble are quantities that influence the nature of the system's internal states such as the total number of particles in the system (symbol: N), the system's volume (symbol: V), as well as the total energy in the system (symbol: E). This ensemble is therefore sometimes called the NVE ensemble, as each of these three quantities is a constant of the ensemble. $\endgroup$
    – Q.stion
    Feb 18, 2019 at 16:11
  • $\begingroup$ Is it also possible that additionally T is constant? I thought this could be true if there is a system with let's say only a single macrostate. $\endgroup$
    – Q.stion
    Feb 18, 2019 at 16:12

1 Answer 1

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Each ensemble of Statistical Mechanics is characterized by a set of thermodynamic variables which are fixed. Although Statistical Mechanics textbooks usually present the case of systems which can be described within a fluid thermodynamic description ( using $P,V,T,E,\mu, N$ as independent state variables, there is no reason, and in practice does not happen that one is confined to physical systems described only by these variables.

Other variables may be added or may be used in place of this list, depending on the set of state variables required for the description of the system. For example, if the fluid system may be magnetized (ferrofluids), canonical ensemble will be characterized by $T,V,N,{\bf M}$, where ${\bf M}$ is the density of magnetic moment. A solid system should be characterized by the strain tensor instead of the volume only.

Moreover, even staying in the class of fluid systems, multicomponent systems require the introduction of the concentrations.

Of course, in correspondence of each of such unusual ensembles, one needs to be able to write a Hamiltonian depending on the new degrees of freedom

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