Consider the specific heat (in statistical sense, as energy fluctuation in the canonical ensemble) of a complex model, something similar to a spin glass. Is the specific heat defined on fluctuations about a specific (local) equilibrium state, or on all possible fluctuations given values for the parameters of the Hamiltonian (including temperature)?
The question is not trivial because there are many possible local equilibria in a spin glass for a given temperature. Should I let the energy fluctuate between multiple ones?
Let me clarify using the computational point of view. Suppose I sample states from my spin glass, compute their energies and the variance of the latter. The histogram of energies looks like this:
Should I consider the peak on the right while computing the specific heat? I suspect more peaks may appear the more I sample, giving me unphysical jumps in the specific heat dependant on the number of sampling steps.
Please do not answer this question using specific spin glass models, as mine may be different, unless you want to use them as examples.
EDIT As it was pointed out, this depends on how we define the specific heat, and why we want to use it for, so I specify that I'm studying the behaviour of Cv to look for criticality-related peaks.