  With the help of a general expression of the entropies in extensive and
nonextensive systems, some important relations between thermodynamics and
statistical mechanics are revealed through the views of thermodynamics and
statistic physics. These relations are proved through the MaxEnt approach once
again. It is found that for a reversible isothermal process, the information
contained in the first and second laws of thermodynamics and the MaxEnt
approach is equivalent. Moreover, these relations are used to derive the
probability distribution functions in nonextensive and extensive statistics and
calculate the generalized forces of some interesting systems. The results
obtained are of universal significance.
