Quantum thermodynamics: emergence of thermodynamic behavior by Jochen Gemmer, M. Michel, Günter Mahler

By Jochen Gemmer, M. Michel, Günter Mahler

This introductory textual content treats thermodynamics as an incomplete description of quantum structures with many levels of freedom. Its major aim is to teach that the method of equilibrium—with equilibrium characterised by way of greatest lack of knowledge concerning the open approach of interest—neither calls for that many debris neither is the appropriate method of partitioning, appropriate for the salient gains of equilibrium and equilibration. moreover, the textual content depicts that it's certainly quantum results which are at paintings in bringing approximately thermodynamic habit of modest-sized open platforms, therefore making Von Neumann’s inspiration of entropy look even more greatly worthwhile than occasionally feared, some distance past really macroscopic platforms in equilibrium.

This considerably revised and improved moment version can pay extra consciousness to the transforming into variety of functions, in particular non-equilibrium phenomena and thermodynamic techniques of the nano-domain. furthermore, to enhance clarity and decrease unneeded technical information, a wide section of this ebook has been completely rewritten.

From the experiences of the 1st edition:

This textbook offers a complete procedure, from a theoretical physics standpoint, to the query of emergence of thermodynamic habit in quantum systems... [Its] energy lies within the cautious improvement of the suitable innovations, specifically the query how huge a approach has to be to express thermodynamic habit is addressed. Luc Rey-Bellet (Amherst, MA), Mathematical stories 2007e

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Additional info for Quantum thermodynamics: emergence of thermodynamic behavior within composite quantum systems

Sample text

If we demand the packages to be smaller in the beginning, their spreading gets even worse. Considering this, it is questionable whether any explanation based on Hamiltonian dynamics in phase space or μ-space (cf. Sect. 1) can ever be a valid foundation of thermodynamics at all. This insufficiency of the classical picture becomes manifest at very low temperatures (freezing out inner degrees of freedom) and it is not obvious why it should become valid at higher temperatures even if it produces good results.

To understand this assumption in more detail, we consider an infinitesimal time step of the evolution of some special function f depicted in Fig. 1. We restrict ourselves here to a two-dimensional “gas”; nevertheless, the μ-space is already four-dimensional, thus we have to visualize f by projections. The special function f corresponds to a situation with all particles concentrated in one cell in configuration space but moving in opposite directions with the same velocity. By some “center of mass” coordinate transformation any collision process may by mapped on this one.

J. html (2002) 23 7. D. Mahan, Many-Particle Physics, 3rd edn. (Plenum Press, New York, London, 2000) 32 8. E. Jaynes, Phys. Rev. 106, 620 (1957) 37 9. E. Jaynes, Phys. Rev. 108, 171 (1957) 37 Chapter 4 Brief Review of Pertinent Concepts Given the success of Ludwig Boltzmann’s statistical approach in explaining the observed irreversible behavior of macroscopic systems . . , it is quite surprising that there is still so much confusion about the problem of irreversibility. — J. L. Lebowitz [1] Boltzmann’s ideas are as controversial today, as they were more than hundred years ago, yet they are still defended (Lebowitz 1993).

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