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Dissipation in a thermodynamic system is an irreversible loss of ability to do work in a system; in other words, the energy gets converted into its forms which are inaccessible for work eventually due to the second law of thermodynamics. For example, dissipation of mechanical energy to the heat absorbed by the environment via friction.
Often dissipation can be accounted for by working with non-Hermitean effective Hamiltonians.
Wikipedia: Dissipation
Richard P. Feynman, F. L. Vernon, Jr.: The theory of a general quantum system interacting with a linear dissipative system, Annals of Physics 24 (1963) 118–173, reprinted in Annals of Physics 281(1-2) 547–607 (2000) doi:10.1006/aphy.2000.6017
Leggett, A. J., Chakravarty, S. D. A. F. M. G. A., Dorsey, A. T., Fisher, M. P., Garg, A., & Zwerger, W. Dynamics of the dissipative two-state system, Reviews of Modern Physics, 59(1) (1987) 1
A. Kossakowski, On quantum statistical mechanics of non-Hamiltonian systems, Reports on Mathematical Physics, 3(4) (1972) 247–274 doi
G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48(2) (1976) 119–130 doi
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