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# Nonequilibrium Thermodynamics of Dissipative Quantum Systems

# Main content

In the context of solid state-based quantum information processing, external control in quantum optics, quantum transport through meso- and nanoscale structures, quantum tunneling in macroscopic systems, quantum Brownian motors, and biological reactions, for example, quantum dissipation is an important subject. We have proposed a general thermodynamic framework for dissipative quantum systems in weak contact with classical equilibrium and nonequilibrium environments that leads to quantum master equations [1]. The proposed formulation is guided by classical nonequilibrium thermodynamics, based entirely on geometric concepts and, in principle, applicable to arbitrarily complex quantum subsystems and classical environments. Geometric structures are employed to construct reversible and irreversible dynamics from energy and entropy landscapes. An important generalization of these ideas has been developed in terms of modular dynamical semigroups [2].

A most important feature of the resulting quantum master equation is its nonlinearity. Some simple illustrations have been given [3]. Simulation techniques for thermodynamic master equations have been developed in [4] and [5]. The classical environment need not be a heat bath. The coupling of a quantum system to a simple time-dependent environment has been explored in [6]. Thermodynamically founded quantum master equations also help to resolve to a long-standing debate on the supposed failure of the fluctuation dissipation theorem [7]. For applications such as quantum computation, ultralong coherence associated with biexponential decay is a very promising feature; the nonlinear thermodynamic master equation can reproduce the key experimental findings [8]. Finally, the new quantum master equation is also the basis for dissipative quantum field theory.

## References

- H.C. Öttinger,
*The geometry and thermodynamics of dissipative quantum systems*, Europhys. Lett. 94 (2011) 10006, 1-6. - D. Taj, H.C. Öttinger,
*Natural approach to quantum dissipation*, Phys. Rev. A 92 (2015) 062128, 1-5. - H.C. Öttinger,
*Nonlinear thermodynamic quantum master equation: Properties and examples*, Phys. Rev. A 82 (2010) 052119, 1-11. - H.C. Öttinger,
*Stochastic process behind nonlinear thermodynamic quantum master equation. I. Mean-field construction*, Phys. Rev. A 86 (2012) 032101, 1-5. - J. Flakowski, M. Schweizer, H.C. Öttinger,
*Stochastic process behind nonlinear thermodynamic quantum master equation. II. Simulation*, Phys. Rev. A 86 (2012) 032102, 1-9. - M. Osmanov, H.C. Öttinger,
*Open quantum systems coupled to time-dependent classical environments*, Int. J. Thermophys. 34 (2013) 1255-1264. - J. Flakowski, M. Osmanov, D. Taj, H.C. Öttinger,
*Time-driven quantum master equations and their compatibility with the fluctuation dissipation theorem*, Phys. Rev. A 90 (2014) 042110, 1-10. - J. Flakowski, M. Osmanov, D. Taj, H.C. Öttinger,
*Biexponential decay and ultralong coherence of a qubit*, Europhys. Lett. 113 (2016) 40003, 1-6.