At atomic level, photons can be absorbed by the atomic or molecule electrons, and an electronic energy transition occurs between the energy levels of two atomic stationary states. Then, the photons can also be emitted by the excited electrons when they jump down into the energy level of the original stationary state. During this phenomenon, the electrons seem to follow a reversible energetic path, because they come back to the original stationary state of low energy level . Indeed, when we consider a single atom or molecule, the energy perturbation of the center of mass is of the order of 10 -13 J, while a usual energy for the electron transition, between two atomic or molecule levels, is of the order of 10 -8 J, with an excited state lifetime of the order of 10 -8 s . Consequently, this approximation (not considering the effect of the atomic nucleus) is usually introduced. But, we stress that it is only an approximation , that cannot be considered in the analysis of the irreversibility, because it requires some considerations just on the role of the nucleus, during the photon-atomic electron interaction . As a consequence of the interaction between the atomic or molecule electron and the photon, a footprint occurs in the atom or molecule. The results obtained in Refs. point out that the interaction between a photon and an electron in an atom affects the energy level both of the electron and of the center of mass of the atom in accordance with the theoretical and experimental results summarised in Refs. . So, the macroscopic irreversibility is the result of the microscopic irreversibility due to the photon-electron interaction, which is the interaction between the environmental electromagnetic waves and the matter. Following the results obtained in the thermodynamic analysis of electromagnetic fields , this interaction can be expressed in terms of the entropy production, and of the entropy production rate. But, the ratio between the entropy production and the entropy production rate is a time. In analogy with analytical mechanics, where position and velocity can be used as independent variables for the state space, we introduce the entropy production σ and the entropy production rate Σ, as the independent variables of the state space Ω = {(σ, Σ)}, used to study the behaviour of the photon-atomic electron interaction. So, we can introduce the definition of time as follows :