text: In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.
  To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.
  It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.
  If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."
  If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.
  If the mesoscopic system is further repeatedly divided, eventually a  microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.
  The statement that the system is its own internal thermodynamic equilibrium may be taken to mean that indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values. Thus the statement, that a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables, is far far more informative than a statement that a set of single simultaneous measurements of those functions of state have those same values. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.