Hi, This question is probably a dumb one but I admit that I am quite perturbed with this issue. Indeed, I don't understand why canonical ensembles like the microcanonical ensemble or the canonical one are called "equilibrium ensemble". I do agree that they correspond to steady measures of probability but why do they reffer only to equilibrium is a mystery for me. The reason of my misunderstanding is that microstates corresponding to out of equilibrium macrostates are allowed in these ensembles. For example microstates corresponding to non uniform density are allowed in the microcanonical ensemble (for perfect gazes for example) where all microstates in the hypersurface of constant energy (with a given uncertainty) are allowed. Now, I thought that, at equilibrium, the density was uniform in an homogen fluid... I am more dubious when, searching for answers about foundations of statistical mechanics, I read papers and courses where the Boltzmann H theorem or more generaly the second principle are correctly (it seems) understood assuming that all microstates of the surface at constant energy are "visited" with the same probability (the microcanonical ensemble appears again in a general context this time) and that the macrostate of equilibrium correspond to an overwelming number of microstates compared to non equilibrium microstates. Thinking a lot about it, it leads me to the conclusion, perhaps the wrong one, that the canonical ensemble distributions refer to systems that can be observed during an infinite time which lead to the equiprobability "principle" (somewhat explain with the historical idea of ergodicty) and the time independence of the distributions but not especially to the equilibrium (macro)states of these systems. What is your opinion about that ? Thank you for any comments that could help me !