  One of the defining properties of an open quantum system is the variation of
its purity in time. We derive speed limits on the rate of purity change for
systems coupled to a Markovian environment. Our speed limits are based on
Liouville space where density matrices are represented as vectors. This
approach leads to speed limits that are always tighter compared to their
parallel speed limits in Hilbert space. These bounds depend solely on the
generators of the nonunitary dynamics and are independent of the particular
states of the systems. Thus, they are perfectly suited to investigate
dephasing, thermalization, and decorrelation processes of arbitrary states. We
show that our speed limits can be attained and are therefore tight. As an
application of our results we study correlation loss, and the speed of
classical and quantum correlation erasure in multi-particle system.
