Quantum thermodynamics: emergence of thermodynamic behavior within composite quantum systems

Jochen Gemmer, M. Michel, Günter Mahler (auth.)3540705090, 9783540705093, 3540705104, 9783540705109

This introductory text treats thermodynamics as an incomplete description of quantum systems with many degrees of freedom. Its main goal is to show that the approach to equilibrium—with equilibrium characterized by maximum ignorance about the open system of interest—neither requires that many particles nor is the precise way of partitioning, relevant for the salient features of equilibrium and equilibration. Furthermore, the text depicts that it is indeed quantum effects that are at work in bringing about thermodynamic behavior of modest-sized open systems, thus making Von Neumann’s concept of entropy appear much more widely useful than sometimes feared, far beyond truly macroscopic systems in equilibrium.

This significantly revised and expanded second edition pays more attention to the growing number of applications, especially non-equilibrium phenomena and thermodynamic processes of the nano-domain. In addition, to improve readability and reduce unneeded technical details, a large portion of this book has been thoroughly rewritten.

From the reviews of the first edition:

This textbook provides a comprehensive approach, from a theoretical physics point of view, to the question of emergence of thermodynamic behavior in quantum systems… [Its] strength lies in the careful development of the relevant concepts, in particular the question how large a system needs to be to exhibit thermodynamic behavior is addressed. Luc Rey-Bellet (Amherst, MA), Mathematical Reviews 2007e

Table of contents :
Front Matter….Pages 1-13
Front Matter….Pages 1-1
Introduction….Pages 3-6
Basics of Quantum Mechanics….Pages 7-22
Basics of Thermodynamics and Statistics….Pages 23-39
Brief Review of Pertinent Concepts….Pages 41-62
Front Matter….Pages 63-63
The Program for the Foundation of Thermodynamics….Pages 65-68
Outline of the Present Approach….Pages 69-76
Dynamics and Averages in Hilbert Space….Pages 77-83
Typicality of Observables and States….Pages 85-93
System and Environment….Pages 95-105
The Typical Reduced State of the System….Pages 107-117
Entanglement, Correlations and Local Entropy….Pages 119-127
Generic Spectra of Large Systems….Pages 129-138
Temperature….Pages 139-148
Pressure and Adiabatic Processes….Pages 149-155
Quantum Mechanical and Classical State Densities….Pages 157-171
Equilibration in Model Systems….Pages 173-188
Front Matter….Pages 189-189
Brief Review of Relaxation and Transport Theories….Pages 191-199
Projection Operator Techniques and Hilbert Space Average Method 1 ….Pages 201-213
Finite Systems as Thermostats….Pages 215-225
Projective Approach to Dynamical Transport….Pages 227-240
Front Matter….Pages 189-189
Open System Approach to Transport 1 ….Pages 241-253
Front Matter….Pages 255-255
Purity and Local Entropy in Product Hilbert Space….Pages 257-261
Observability of Intensive Variables….Pages 263-274
Observability of Extensive Variables….Pages 275-289
Quantum Thermodynamic Processes….Pages 291-313
Back Matter….Pages 1-29