We analyze the dynamics of squeezing in a ballistic quantum wire with Rashba spin-orbit interaction in the presence of both strong and weak magnetic fields and for different initial states of the system. Compared to the more standard measure of squeezing based on variances, we show that entropy squeezing is a more sensitive measure. Our results show that there is a strong relationship between the spin-orbit interaction and the strength of entropy squeezing. Furthermore, there is a relationship between the initial state and the number of squeezed components. This allows new knobs to control the strength and the component of entropy squeezing in a nanowire system.