  Quantum correlations are at the core of quantum mechanics and play a crucial
role in various fields. While bipartite quantum correlations have been
extensively studied, multipartite quantum correlations in many-body systems
remain elusive due to their complex structure. In particular, a primary
challenge lies in the fact that the calculation of multipartite quantum
correlation measure often requires exponential cost. In this work, we tackle
this problem by adopting a thermodynamic approach; we introduce a measure of
multipartite quantum correlations based on the difference in extractable
thermodynamic work by global operations and local operations and classical
communication (LOCC). This can be regarded as a multipartite generalization of
the work deficit, which has attracted attention as a thermodynamic measure of
bipartite quantum correlation. A distinguishing feature of the thermodynamic
approach to multipartite quantum correlation is that we can compare the degree
of quantum correlations with clear operational meaning. Importantly, we develop
an efficient calculation method of the multipartite work deficit. This
efficient method works for a special class of quantum many-body systems
described by matrix product states (MPS), where the numerical cost is shown to
be proportional to the system size, significantly reducing the exponential cost
required for the direct calculations. We demonstrate this efficient method in
the AKLT state and the cluster state, and analytically obtain the exact values
of this measure. We further show that a quantum phase transition described by
MPS is well captured by the multipartite work deficit. This shows that the
multipartite work deficit does not only highlight the fundamental connection
between multipartite quantum correlations and quantum thermodynamics, but also
serves as an efficiently-computable probe of the structures of quantum
many-body systems.
