Negative specific heat, phase transition and particles spilling from a potential well

For a finite number of noninteracting particles in a box with a potential well in the center, the microcanonical kinetic energy in dependence on the total energy as it is negative can be classified into three categories. The first exhibits a monotonical rise and the specific heat is positive. The second shows a diminishing sawtooth wave with a global rise. The last corresponds to the extreme case and takes the regular sawtooth wave form. The sawtooth wave portion associates periodically a kinetic energy fall in spite of an increase of the total energy; and we attribute to such a fall the negative specific heat. The phase transition can be defined when the relatively dense particle state in the well and relatively dilute particle state in the rest volume of the box coexist, and the appearance of the negative specific heat is sufficient but not necessary for the onset of the phase transition.