While reading Gibbs' Elementary Principles in Statistical Mechanics I came across this footnote:

The most simple test of the equality of temperature of two bodies is that they remain in equilibrium when brought into thermal contact. Direct thermal contact implies molecular forces acting between the bodies. Now the test will fail unless the energy of these forces can be neglected in comparison with the other energies of the bodies. Thus, in the case of energetic chemical action between the bodies, or when the number of particles affected by the forces acting between the bodies is not negligible in comparison with the whole number of particles (as when the bodies have the form of exceedingly thin sheets), the contact of bodies of the same temperature may produce considerable thermal disturbance, and thus fail to afford a reliable criterion of the equality of temperature.


I think I understand what he's saying here, at least from a theoretical standpoint. But the second example is a bit confusing to me: what does happen if we take two thin foils in termal contact with two reservoirs at the same temperature and bring them into contact? Does the combined system "leave" the canonical distribution and be at an unspecified temperature for a while? And, most important, is this something that comes from experience or is it just a thought experiment?


  • $\begingroup$ Unless I'm misunderstanding the sentence, in the described failure case the energies will not be additive, i.e. the energy of the entire system will not be the energy of sheet 1 plus that of sheet 2, but rather there will be a significant nonlinear component. People are interested in similar system when dealing with long range interactions, and Tsallis entropies and the like. As a simpler example, you can think of surface tension, where this extra energy component can be described simply by adding a new thermodynamical force (but you need an extra variable). $\endgroup$ – alarge May 17 '15 at 20:43

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