  We provide a pure state formulation for hydrodynamic dynamics of isolated
quantum many-body systems. A pure state describing quantum systems in local
thermal equilibrium is constructed, which we call a local thermal pure quantum
($\ell$TPQ) state. We show that the thermodynamic functional and the
expectation values of local operators (including a real-time correlation
function) calculated from the $\ell$TPQ state converge to those from a local
Gibbs ensemble in the large fluid-cell limit. As a numerical demonstration, we
investigate a one-dimensional spin chain and observe the hydrodynamic
relaxation obeying the Fourier's law. We further prove the second law of
thermodynamics and the quantum fluctuation theorem, which are also validated
numerically. The $\ell$TPQ formulation gives a useful theoretical basis to
describe the emergent hydrodynamic behavior of quantum many-body systems
furnished with a numerical efficiency, being applicable to both the
non-relativistic and relativistic regimes.
