A novel thermostatistical approach to describe hot deformation of unary and multicomponent FCC alloys undergoing dynamic recrystallization (DRX) is presented. The approach incorporates an additional softening effect to the Kocks-Mecking equation, which becomes active once a critical incubation strain for recrystallization is achieved. Multicomponent effects are incorporated into the equation to account for solid solution strengthening and recrystallization effects. The dislocation density evolution with strain can be prescribed as a function of temperature, strain rate and composition. The presented unified approach describes stages II, III and IV of deformation, the latter being substituted by DRX when this becomes energetically favourable. It recovers the stress values as steady state is approached, and captures well the temperature-strain rate-composition dependency of DRX allowing to map the conditions under which it occurs. The theory successfully describes the dynamic recrystallization behaviour of Cu, Ni, Ni30Fe, Ni21Cr, Fe30Ni, Fe18Cr8Ni, Fe25Cr20Ni and Ni21Cr8Mo3Nb. Input to the model are only physical parameters and thermodynamic information from well accepted databases. It is shown that the design of alloys for tailored DRX behaviour is possible under this formulation.