  In this work, we show that a universal quantum work relation for a quantum
system driven arbitrarily far from equilibrium extend to
$\mathcal{PT}$-symmetric quantum system with unbroken $\mathcal{PT}$ symmetry,
which is a consequence of microscopic reversibility. The quantum Jarzynski
equality, linear response theory and Onsager reciprocal relations for the
$\mathcal{PT}$-symmetric quantum system are recovered as special cases of the
universal quantum work relation in $\mathcal{PT}$-symmetric quantum system. In
the regime of broken $\mathcal{PT}$ symmetry, the universal quantum work
relation does not hold as the norm is not preserved during the dynamics.
