  We consider the thermodynamic properties of the squeezed vacuum state of a
frequency--modulated quantum harmonic oscillator. We analytically relate the
squeezing parameter to the irreversible work and the degree of nonadiabaticity
of the frequency transformation. We furthermore determine the optimal
modulation that leads to maximal squeezing, and discuss its implementation as
well as the detection of squeezing in single cold ion traps.
