  It is well known that, in the context of general relativity, an unknown kind
of matter that must violate the strong energy condition is required to explain
the current accelerated phase of expansion of the Universe. This unknown
component is called dark energy and is characterized by an equation of state
parameter $w=p/\rho<-1/3$. Thermodynamic stability requires that $3w-d\ln
|w|/d\ln a\ge0$ and positiveness of entropy that $w\ge-1$. In this paper we
proof that we cannot obtain a differentiable function $w(a)$ to represent the
dark energy that satisfies these conditions trough the entire history of the
Universe.
