It seems to me that for some thermodynamic variables it makes sense to talk of systems in contact with different values of these variables. An example is temperature. We can the problem of two systems in contact with different temperatures. However, I am not sure if this is the case for all thermodynamic variables. Consider for instance the pressure. How would you treat a system of two gasses in contact with different pressures - for me it doesn't make sense. What property of the temperature (which is not a property of pressure) makes us able to treat it as described above? The question came to be because chemical potential was treated as temperature where you had two systems in contact with different chemical potentials. Is this allowed?