Uncertainty Relations in Statistical Mechanics: a numerical study in small lattice systems

We have analyzed the validity of uncertainty relations between the fluctuations of thermodynamically conjugated extensive and intensive variables within the field of statistical mechanics. Analysis is presented for two particular examples of small lattice systems that are in contact with reservoirs of comparable sizes: an Ising paramagnet and an Ising ferromagnet. The numerical results enable determination of the range of applicability of the proposed relations. Due to the fact that the examples correspond to systems described by discrete variables, the uncertainty relations are not valid if the probability of boundary states is too high.