Quantum thermodynamics

Quantum thermodynamics is a topic in theoretical physics that concerns the combination of classical thermodynamics and quantum mechanics into a coherent whole. It studies, for example, how a quantum mechanical system interacts with a macroscopic system in thermodynamic equilibrium, such as a heat bath. A important question in quantum thermodynamics is the extent to which the laws of thermodynamics continue to hold as one progresses from quantum systems with a macroscopic number of degrees of freedom, which are well-described by quantum statistical mechanics, to quantum systems with few degrees of freedom, which are well described by quantum mechanics itself.
History
The first attempt to combine thermodynamics with the hypothesis of a quantized state was in 1901 when Max Planck outlined the "quantum hypothesis", i.e. that the energy of atomic systems can be quantized, and studied the effects of quantization on the radiation spectrum of a blackbody in thermal equilibrium. See the history of quantum mechanics for more details.
Approaches
Coupling to a macroscopic system
One approach to quantum thermodynamics is to couple a small quantum system to a macroscopic system and investigate consequences of their interaction. There are two general methods for studying such systems. The "Hamiltonian"" method is to treat the small and macroscopic systems as a composite quantum system and study its ergodic properties. The Liouvillian operator associated with the composite system contains in its spectrum the ergodic behavior of the system, which provides a window into the thermodynamic aspects of the system.
The "Markovian" method is to model the macroscopic system as producing an effective stochastic force acting upon the small quantum system. For instance, a small quantum system coupled to a heat bath can be modeled using a quantum Langevin equation. Such coupling can lead to quantum decoherence. The Markovian method is also sometimes called a quantum noise approach because it can be thought of as perturbing the Schroedinger equation for the small quantum system with a quantum noise term.
Keenan model
The theory of quantum statistical mechanics (QSM) is very successful in explaining many physical phenomena and provides for a basis to understand thermodynamics. But the Keenan approach to quantum thermodynamics at MIT (named for physicist Joseph Henry Keenan) recognizes that the postulates underlying QSM are problematic to justify in a rigorous manner starting from only quantum mechanics. The approach seeks to redress this problem by creating a formalism that contains elements of both quantum mechanics and thermodynamics at the microscopic level. The density operator describing a statistical ensemble in QSM is reinterpreted as a quantum state operator obeying a nonlinear evolution equation that contains a dissipation term. Both quantum mechanics and QSM can be shown to be special cases of this formalism. The Keenan approach has not yet seen adoption by the mainstream physics community.

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