  The phenomenon of quantum entanglement underlies several important protocols
that enable emerging quantum technologies. Entangled states, however, are
extremely delicate and often get perturbed by tiny fluctuations in their
external environment. Certification of entanglement is therefore immensely
crucial for the successful implementation of protocols involving this resource.
In this work, we propose a set of entanglement criteria for multi-qubit systems
that can be easily verified by measuring certain thermodynamic quantities. In
particular, the criteria depend on the difference in optimal global and local
works extractable from an isolated quantum system under global and local
interactions, respectively. As a proof of principle, we demonstrate the
proposed scheme on nuclear spin registers of up to 10 qubits using the Nuclear
Magnetic Resonance architecture. We prepare noisy Bell-diagonal state and noisy
Greenberger-Horne-Zeilinger class of states in star-topology systems and
certify their entanglement through our thermodynamic criteria. Along the same
line, we also propose an entanglement certification scheme in many-body systems
when only partial or even no knowledge about the state is available.
