If we account for the displacement of each particle in the calculation of the total work that is done by the system, then one can see that all the energy is preserved and we receive the equality (∆A sys = W sur ) regardless of the irreversibility of the process in macroscopic scale. To clarify this, we choose a path to take us toward considering the microscopic works in our calculations with the aid of statistical mechanics. To do this, we use Boltzmann's definition of entropy to statistically calculate the net entropy of a microcanonical ensemble of N independent particles where all the states are equally probable: