  When studying the thermodynamic properties of mesoscopic systems the most
appropriate microcanonical entropy is the volume entropy, i.e. the logarithm of
the volume of phase space enclosed by the hypersurface of constant energy. For
systems with broken ergodicity, the volume entropy has discontinuous jumps at
values of energy that correspond to separatrix trajectories. Simultaneously
there is a convex intruder in the entropy function and a region of negative
specific heat below such critical energies. We illustrate this with a simple
model composed of a chain of 3 particles which interact via a Lennard-Jones
potential.
