  The recently introduced concept of timelike entanglement entropy has sparked
a lot of interest. Unlike the traditional spacelike entanglement entropy,
timelike entanglement entropy involves tracing over a timelike subsystem. In
this work, we propose an extension of timelike entanglement entropy to
Euclidean space ("temporal entanglement entropy"), and relate it to the
renormalization group (RG) flow. Specifically, we show that tracing over a
period of Euclidean time corresponds to coarse-graining the system and can be
connected to momentum space entanglement. We employ Holography, a framework
naturally embedding RG flow, to illustrate our proposal. Within cutoff
holography, we establish a direct link between the UV cutoff and the smallest
resolvable time interval within the effective theory through the irrelevant
$T\bar T$ deformation. Increasing the UV cutoff results in an enhanced
capability to resolve finer time intervals, while reducing it has the opposite
effect. Moreover, we show that tracing over a larger Euclidean time interval is
formally equivalent to integrating out more UV degrees of freedom (or lowering
the temperature). As an application, we point out that the temporal
entanglement entropy can detect the critical Lifshitz exponent $z$ in
non-relativistic theories which is not accessible from spatial entanglement at
zero temperature and density.
