  The connections between thermodynamics and quantum information processing are
of paramount importance. Here, we address a bipartite entanglement via
extracted work in a cavity magnomechanical system contained inside an yttrium
iron garnet (YIG) sphere. The photons and magnons interact through an
interaction between magnetic dipoles. A magnetostrictive interaction, analogous
to radiation pressure, couple's phonons and magnons. The extracted work was
obtained through a device similar to the Szil\'ard engine. This engine operates
by manipulating the photon-magnon as a bipartite quantum state. We employ
logarithmic negativity to measure the amount of entanglement between photon and
magnon modes in steady and dynamical states. We explore the extracted work,
separable work, and maximum work for squeezed thermal states. We investigate
the amount of work extracted from a bipartite quantum state, which can
potentially determine the degree of entanglement present in that state.
Numerical studies show that entanglement, as detected by the extracted work and
quantified by logarithmic negativity, is in good agreement. We show the
reduction of extracted work by a second measurement compared to a single
measurement. Also, the efficiency of the Szilard engine in steady and dynamical
states is investigated. We hope this work is of paramount importance in quantum
information processing.
