Detailed definition of temperature for nonequilibrium thermodynamics: Essential for information and quantum thermodynamics

The detailed definition of temperature has been the fundamental subject for the nonequilibrium thermodynamic theory essentially for information and quantum thermodynamic theories. The present definition of temperature is based on equilibrium thermodynamics because it is defined under the irreversible adiabatic condition using the local-equilibrium assumption. The temperature of a nonequilibrium state must be defined under the nonadiabatic condition for nature or the world. Nature is reversible in time in kinetics and phase transition. The world is irreversible in time in information and life under the second law of thermodynamics. The world is a temporal stage with an appropriate time scale upon the irreversible process of the universe with a vast time scale. The temperature in the world retaining information and life was defined under the nonadiabatic condition against that in the universe under the adiabatic condition. Information has an essential role in quantum thermodynamics through the quantum superposition principle, which enables us to carry out quantum computations.