Equilibrium = homogeneity of the intensive parameters? It is obvious, that if all intensive parameters of an isolated thermodynamic system are homogeneous then the system is in equilibrium. But, what is the situation with the reverse statement? Is it true, that if an isolated thermodynamic system is in equilibrium, then all intensive parameters of it must be homogeneous? I say a counter-example: a grape in a glass water. If the grape is strong enough that does not crack, then the pressure inside the grape will be greater than in the surrounding water. So, it seems, that an isolated thermodynamic system can be in equilibrium, even the pressure isn't homogeneous inside. But, what about the other intensive parameters, e.g. with the temperature? Can be an isolated system in thermodynamic equilibrium if the temperature isn't homogeneous inside?