  In recent years, dynamical quantum phase transitions (DQPTs) have emerged as
a useful theoretical concept to characterize nonequilibrium states of quantum
matter. DQPTs are marked by singular behavior in an \textit{effective free
energy} $\lambda(t)$, which, however, is a global measure, making its
experimental or theoretical detection challenging in general. We introduce two
local measures for the detection of DQPTs with the advantage of requiring fewer
resources than the full effective free energy. The first, called the
\textit{real-local} effective free energy $\lambda_M(t)$, is defined in real
space and is therefore suitable for systems where locally resolved measurements
are directly accessible such as in quantum-simulator experiments involving
Rydberg atoms or trapped ions. We test $\lambda_M(t)$ in Ising chains with
nearest-neighbor and power-law interactions, and find that this measure allows
extraction of the universal critical behavior of DQPTs. The second measure we
introduce is the \textit{momentum-local} effective free energy $\lambda_k(t)$,
which is targeted at systems where momentum-resolved quantities are more
naturally accessible, such as through time-of-flight measurements in ultracold
atoms. We benchmark $\lambda_k(t)$ for the Kitaev chain, a paradigmatic system
for topological quantum matter, in the presence of weak interactions. Our
introduced local measures for effective free energies can further facilitate
the detection of DQPTs in modern quantum-simulator experiments.
