  Producing and certifying entanglement between distant qubits is a highly
desirable skill for quantum information technologies. Here we propose a new
strategy to monitor and characterize entanglement genesis in a half parity
measurement setup, that relies on the continuous readout of an energetic
observable which is the half-parity observable itself. Based on a
quantum-trajectory approach, we theoretically analyze the statistics of
energetic fluctuations for a pair of continuously monitored qubits. We
quantitatively relate these energetic fluctuations to the rate of entanglement
produced between the qubits, and build an energetic-based estimator to assess
the presence of entanglement in the circuit. Remarkably, this estimator is
valid at the single-trajectory level and shows to be robust against finite
detection efficiency. Our work paves the road towards a fundamental
understanding of the stochastic energetic processes associated with
entanglement genesis, and opens new perspectives for witnessing quantum
correlations thanks to quantum thermodynamic quantities.
