 The method of shortcuts to adiabaticity is applied to non-equilibrium systems for unitary dynamics, where the system Hamiltonian is separated into two parts that define adiabatic states and prevent non-adiabatic transitions. This property is used to separate the entropy production into two parts, which represents the Pythagorean theorem for the Colbach-Liebler divergence and an information geometric interpretation is obtained. Additionally, a lower bound of the entropy is studied to derive a trade-off relation between time, entropy, and state distance. This article was authored by Kazataka Tokohoshi.