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'''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]]<ref>Planck, Max. (1901). "''[http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html On the Law of Distribution of Energy in the Normal Spectrum]''". [[Annalen der Physik]], vol. 4, p. 553 ff.</ref>. 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<ref>W. Jaksic, C.-A. Pillet: “On a model for quantum friction I: Fermi’s golden
rule and dynamics at zero temperature”, Annales Henri Poincar ́ Physique Theorique 62 (1995), p. 47-68.</ref><ref>W. Jaksic, C.-A. Pillet: “On a model for quantum friction II: Fermi’s golden rule and dynamics at positive temperature”, Communications in Mathematical Physics 176 (1996), p. 619-644.</ref><ref> W. Jaksic, C.-A. Pillet: “On a model for quantum friction III: Ergodic properties of the spin-boson system”, Communications in Mathematical Physics 178 (1996), p. 627-651.</ref>. 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<ref> S. Attal, Y. Pautrat: From Repeated to Continuous Quantum Interactions. Annales Henri Poincare (Physique Theorique) 7 (2006), p.59-104.</ref>. For instance, a small quantum system coupled to a [[heat bath]] can be modeled using a quantum [[Langevin equation]]<ref>S. Attal, and A. Joye, "The Langevin Equation for a Quantum Heat Bath" , Journal of Functional Analysis , 247, (2007), p. 253-288.</ref>. Such coupling can lead to [[quantum decoherence]]. The Markovian method is also sometimes called a [[quantum noise]] approach<ref>A.C. Gardiner, and P. Zoller, "Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics", Springer, 2004 </ref> 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<ref>C. Kittel, "Elementary Statistical Physics", John Wiley and Sons, 1958, chapters 10 and 23.</ref>. 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<ref>G.N. Hatsopoulos and E.P Gyftopoulos, A unified quantum theory of mechanics and thermodynamics. Part I. Postulates , Foundations of Physics, Vol. 6, 15 (1976)</ref><ref>G.N. Hatsopoulos and E.P Gyftopoulos, A unified quantum theory of mechanics and thermodynamics. Part IIa. Available energy, Foundations of Physics, Vol. 6, 127 (1976).</ref><ref>G.N. Hatsopoulos and E.P Gyftopoulos, A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states, Foundations of Physics, Vol. 6, 439 (1976).</ref><ref>G.N. Hatsopoulos and E.P Gyftopoulos, A unified quantum theory of mechanics and thermodynamics. Part III. Irreducible quantal dispersions , Foundations of Physics, Vol. 6, 561 (1976).</ref>. 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<ref>G.P. Beretta, "What Is Quantum Thermodynamics?", <http://www.ing.unibs.it/~beretta/www.quantumthermodynamics.org/WebSite1.pdf>, 1 Dec. 2011.</ref><ref>J. Maddox, Nature, 316, p. 11 (1985).</ref>.

==See also==
* [[Quantum decoherence]]
{{portal|Physics}}

==References==
<div class="references-small">
<references />
</div>

==Further reading==
<div class="references-small">
#{{cite book | author=Gemmer, J., Michel, M., Mahler, G. | title= Quantum Thermodynamics – Emergence of Thermodynamic Behavior Within Composite Quantum Systems | publisher=Springer | year=2005 | isbn=3-540-22911-6}}
#{{cite book | author=Rudakov, E.S. | title= Molecular, Quantum and Evolution Thermodynamics: Development and Specialization of the Gibbs Method. | publisher=Donetsk State University Press | year=1998 | isbn=966-02-0708-5}}
</div>

==External links==
*[http://staff.science.uva.nl/~nieuwenh/QL2L.html Quantum Thermodynamics and the Gibbs Paradox]
*[http://www.chaos.org.uk/~eddy/physics/heat.html Quantum Thermodynamics]
*[http://www.fh.huji.ac.il/~ronnie/Papers/geva92.pdf On the Classical Limit of Quantum Thermodynamics in Finite Time] [PDF-format]
*[http://www.quantumthermodynamics.org Quantum Thermodynamics] - list of articles related to the Keenan approach
*[http://arxiv.org/ftp/quant-ph/papers/0502/0502150.pdf Quantum thermodynamics and Brownain motion]

[[Category:thermodynamics]]

Quantum thermodynamics - Revision history

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