Nonequilibrium Statistical Thermodynamics – Zubarev

In this post, we will see the book Nonequilibrium Statistical Thermodynamics by D. N. Zubarev.

About the book

In this book an attempt is made to give a unified account of the present state of nonequilibrium statistical thermodynamics as a natural generalization of the equilibrium theory.
From a logical point of view, it would be desirable to develop the statistical theory of nonequilibrium processes first, and treat the theory of statistical equilibrium as its limiting case. Such an approach, however, is scarcely worthwhile at the present time, since nonequilibrium and equilibrium statistical thermodynamics are at very different stages of development. In Chapters I and II, therefore, we give a brief account of the basic ideas of the classi­cal and quantum statistical mechanics of equilibrium systems, to the extent that this is necessary for the derivation of the basic thermodynamic relations for the case of statistical equilibrium.
The purpose of these introductory chapters is to recall the general method of Gibbsian statistical ensembles, since later, in Chapters in and IV, attempts are made to take over the ideas of statistical ensembles to nonequilibrium statistical thermody­namics.

The book was translated from Russian by was published in  by Publishers.

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Chapter 1 Equilibrium Statistical Thermodynamics of Classical Systems 1

§1. Distribution functions 1
§2. Liouville’s equation 5
§3. Gibbsian statistical ensembles 18
§4. The connection between the Gibbsian distributions and the maximum of the information entropy 38
§5. Thermodynamic equalities 46
§6 Fluctuation 55

Chapter 2 Equilibrium Statistical Thermodynamics of Quantum Systems 65

§7. The statistical operator 65
§8. The quantum Liouville equation 73
§9. Gibbsian statistical ensembles in the quantum case 82
§10. The connection between Gibbsian distributions and the maximum of information entropy (quantum case) 100
§11. Thermodynamic equalities 105
§12. Fluctuations in Quantum Systems 115
§13. Thermodynamic equivalence of the Gibbsian statistical ensembles 119
§14. Passage to the classical limit of quantum 129

Chapter 3 Irreversible Processes Induced by Mechanical Perturbations 141

§15. Response of a system to external mechanical perturbations 141
§16. Two-time Green functions 174
§17. Fluctuation-dissipation theorems and dispersion relations 196
§18. Systems of charged particles in an alternating electromagnetic field 220

Chapter 4 The Nonequilibrium Statistical Operator 237

§19. Conservation Laws 242
§20. The local-equilibrium distribution 266
§21. Statistical operator for nonequilibrium systems 301
§22. Tensor, vector and scalar processes 317
§23. Relaxation Processes 360
§24. The statistical operator for relativistic systems and relativistic hydrodynamics 395
§25. Kinetic equations 411
§26. The Kramers—Fokker—Planck equations 424
§27. Extremal properties of the nonequilibrium statistical operator 435

Appendix I Formal Scattering Theory in Quantum Mechanics 453
Appendix II MacLennan’s Statistical Theory of Transport Processes 461
Appendix III Boundary Conditions for the Statistical Operators in the Theory of Nonequilibrium Processes and the Method of Quasi-Averages 465

References 471

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