Two-time temperature Green's functions in statistical physics are introduced as a generalization of Green's functions in quantum field theory. These functions are essential for studying interacting quantum fields and are particularly useful in statistical mechanics for analyzing systems with a large number of particles. The paper discusses the properties and applications of these functions, focusing on their use in irreversible processes, superconductivity, ferromagnetism, and electron-phonon interactions in metals and semiconductors. The functions are defined using time-ordered and time-reversed products of operators, and they allow for the calculation of physical observables in systems at finite temperatures. The paper also highlights the importance of spectral representations and their role in the analysis of Green's functions. The use of two-time Green's functions provides a more accurate description of systems where the energy levels are closely spaced and the temperature is not zero. The paper concludes that these functions are particularly useful for analyzing systems with a large number of particles and for studying phenomena such as superconductivity and ferromagnetism. The paper also discusses the advantages of using two-time Green's functions over traditional Green's functions in statistical mechanics, as they allow for the analytical continuation into the complex plane and are more suitable for describing systems at finite temperatures. The paper provides a detailed discussion of the properties and applications of two-time Green's functions in statistical physics, emphasizing their importance in the study of complex systems.Two-time temperature Green's functions in statistical physics are introduced as a generalization of Green's functions in quantum field theory. These functions are essential for studying interacting quantum fields and are particularly useful in statistical mechanics for analyzing systems with a large number of particles. The paper discusses the properties and applications of these functions, focusing on their use in irreversible processes, superconductivity, ferromagnetism, and electron-phonon interactions in metals and semiconductors. The functions are defined using time-ordered and time-reversed products of operators, and they allow for the calculation of physical observables in systems at finite temperatures. The paper also highlights the importance of spectral representations and their role in the analysis of Green's functions. The use of two-time Green's functions provides a more accurate description of systems where the energy levels are closely spaced and the temperature is not zero. The paper concludes that these functions are particularly useful for analyzing systems with a large number of particles and for studying phenomena such as superconductivity and ferromagnetism. The paper also discusses the advantages of using two-time Green's functions over traditional Green's functions in statistical mechanics, as they allow for the analytical continuation into the complex plane and are more suitable for describing systems at finite temperatures. The paper provides a detailed discussion of the properties and applications of two-time Green's functions in statistical physics, emphasizing their importance in the study of complex systems.