Dissipation in quantum physics

A compact description of the evolution of a many-body quantum system, e.g., a dilute gas, is provided by the generalization of the usual reaction U matrix to a system U matrix. Using this tool, it is demonstrated that in such systems (i) time-reversal-invariant states are unstable and cannot exist in nature or be ‘‘constructed in the laboratory;’’ (ii) the time-reversal invariance of the Hamiltonian leads inexorably to relaxation towards thermal equilibrium of arbitrary nonequilibrium states, i.e., to dissipation, which thus allows the definition of a quantum arrow of time; (iii) the second law of thermodynamics, and hence the complete field of thermodynamics, is a consequence of quantum physics. These results have at their basis the hermiticity of the Hamiltonian and the Heisenberg uncertainty relations.