Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems

J. Gemmer, M. Michel, G. Mahler (auth.)9783540229117, 3-540-22911-6, 3540229116

This extended tutorial essay views thermodynamics as an incomplete description of quantum systems with many degrees of freedom. The 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 it a precise way of partitioning relevant for the salient features of equilibrium and equilibration. Moreover it is indeed quantum effects that are at work in bringing about universal thermodynamic behaviour of modestly sized open systems. Von Neumann`s concept of entropy thus proves to be much more widely useful than something to be feared, and far beyond truly macroscopic systems in equilibrium.

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Table of contents :
1 Introduction….Pages 3-5
2 Basics of Quantum Mechanics….Pages 7-20
3 Basics of Thermodynamics and Statistics….Pages 21-36
4 Brief Review of Pertinent Concepts….Pages 37-58
5 The Program for the Foundation of Thermodynamics….Pages 61-64
6 Outline of the Present Approach….Pages 65-69
7 System and Environment….Pages 71-77
8 Structure of Hilbert Space….Pages 79-89
9 Quantum Thermodynamic Equilibrium….Pages 91-108
10 Interim Summary….Pages 109-112
11 Typical Spectra of Large Systems….Pages 113-122
12 Temperature….Pages 123-131
13 Pressure….Pages 133-141
14 Quantum Mechanical and Classical State Densities….Pages 143-157
15 Sufficient Conditions for a Thermodynamic Behavior….Pages 159-163
16 Theories of Relaxation Behavior….Pages 165-167
17 The Route to Equilibrium….Pages 169-182
18 Equilibrium Properties of Model Systems….Pages 185-219
19 Heat Conduction….Pages 221-234
20 Quantum Thermodynamic Machines….Pages 235-240
21 Summary and Conclusion….Pages 241-244
A Hyperspheres….Pages 247-252
B Hilbert Space Average under Microcanonical Conditions….Pages 253-258
C Hilbert Space Averages and Variances….Pages 259-264
D Power of a Function….Pages 265-266
E Local Temperature Conditions for a Spin Chain….Pages 267-269