As in thermodynamics, the celebrated first law of black hole mechanics relates infinitesimal changes in the properties of nearby equilibrium states of black holes (without reference to any physical process that causes the transition). Using dynamical horizon segments (DHSs), we extend the first law to encompass black holes that can be arbitrarily far from equilibrium. It now refers to finite changes that occur due to physical processes. This extension, together with the generalized second law on DHSs [A. Ashtekar and B. Krishnan, Dynamical horizons and their properties, Phys. Rev. D 68, 104030 (2003)PRVDAQ0556-282110.1103/PhysRevD.68.104030], naturally lead one to identify entropy of dynamical black holes with the area of DHSs.