Abstract
First, a clear presciption for a two-scale potential is provided.
Then, we investigate the thermodynamic and the dynamic properties
of particles interacting via this
potential in order to show the presence of anomalies like the
ones present in water.
We show that, for any chosen shape of a two-scale potential, the
density,
at constant pressure, has a maximum for a certain temperature. The
line
of temperatures of maximum density (TMD) is determined in the
pressure-temperature
phase diagram. Similarly the diffusion constant at a constant
temperature, $D$, has a maximum at a density $\rho_max$ and a
minimum at a density
$\rho_min<\rho_max$. In
the pressure-temperature phase-diagram
the line of temperature of extrema diffusivity (TED)
is related to the TMD line as follows. If the potential is
continuous, the TMD line lies
inside the TED line, if the potential is discontinuous ( lattice
or step-like), the TMD line lies outside the TED line.
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