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R.G.ZARIPOV

DISCRIMINATION INFORMATION

AND DISORDER - ORDER TRANSITIONS

CONTENTS

Preface

Chapter 1. Entropy, information and energy in the statistical theory

1.1. Boltzmann–Gibbs entropy

1.2. The principle of maximum entropy

1.3. Shannon–Wiener entropy and Kullback discrimination information

1.4. The principle of minimum discrimination information

1.5. The statistics and information

Chapter 2. The physical discrimination information and its evolution

2.1. The discrimination information is a degree of microstates in transition in classical and quantum systems

2.2. Work, spontaneous transitions and self-decay

2.3. Informational efficiency of energy transformation

2.4. Induced transitions and self-organization. *I*-theorem

2.5. Boundaries of variation of degree of order. h -theorem

2.6. Transitions for Fermi and Bose gases

2.7. Nonparameteric estimate of degree of order

2.8. Instability of disorder and evolution of discrimination information

2.9. *I*-theorem for relativistic systems

2.10. Thermodynamic probability and discrimination information

Chapter 3. Fluctuations and uncertainty

3.1 The discrimination information and macroscopic distribution function

3.2. Set of thermodynamic operators of fluctuations of physical values

3.3. Statistic fluctuations of jointly measurable values

3.4. Fluctuations of equilibrium microscopic entropy and the discrimination information. Conditions of stability of the equilibrium state

3.5. Statistic estimate of intensive parameters. The uncertainty relation

3.6. General boundary of accuracy of measurement of physical values….

3.7. The uncertainty relation for quantum values. The information and measurement

3.8. Quantum estimate of nonfluctuating parameters

3.9. Equations of equilibrium states of quantum and classical systems

Chapter 4. Nonequilibrium fluctuations and non-Liouvillian dynamics of open systems

4.1. Microscopic entropy production and statistic criterium of evolution of open systems

4.2. The uncertainty relation and non-Liouvillian kinetic equation

4.3. The principle of minimum of variance of microscopic entropy production

4.4. Fluctuation of local-equilibrium microscopic entropy production and stability criterium of states

4.5. Irreversibility and transitions in the non-Liouvillian dynamics of open systems

4.6. Nonequilibrium transitional fluctuations in measurements

4.7. Non-Liouvillian kinetic equation for a system with friction

4.8. Minimum uncertainty state for quantum values

Chapter 5. Informational physical processes and transitions in continuous media

5.1. Balance equation in macroscopic irreversible transitions

5.2. Stationary states and ordering in systems

5.3. Forces and flows in irreversible processes

5.4. Macroscopic criterium of evolution of systems in irreversible transitions

Conclusion

References