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Microcanonical Thermodynamics Phase Transitions in Small Systems 1st Edition by Dieter H E Gross ISBN 9810242158 9789810242152

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Microcanonical Thermodynamics Phase Transitions in Small Systems 1st Edition Dieter H E Gross Digital Instant Download

Author(s): Dieter H E Gross
ISBN(s): 9789810242152, 9810242158
Edition: 1st
File Details: PDF, 11.16 MB
Year: 2001
Language: english
SKU: EB-5857018 Category: Tag:

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ISBN 10: 9810242158 
ISBN 13: 9789810242152
Author: Dieter H E Gross

Boltzmann’s formula S = In[W(E)] defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay — for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and classify phase transitions in small systems. This is all possible within Boltzmann’s original definition of the microcanonical ensemble.Starting from Boltzmann’s formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phase transitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E,N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum.The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum.

Microcanonical Thermodynamics Phase Transitions in Small Systems 1st Table of contents:

0.1 Who is addressed and why
0.2 A necessary clarification
0.3 Acknowledgment
Chapter 1 Introduction
1.1 Phase transitions and thermodynamics in “Small” Systems
1.2 Boltzmann gives the key
1.3 Micro-canonical Thermodynamics describes non-extensive systems
1.4 Some realistic systems: Nuclei and atomic clusters
1.5 Plan of this book
Chapter 2 The Mechanical Basis of Thermodynamics:
2.1 Basic definitions
2.2 The thermodynamic limit the global concavity of s(e n)
2.3 Phase transitions micro-canonically
2.4 Second Law of Thermodynamics and Boltzmann’s entropy
Chapter 3 Micro-canonical thermodynamics of Phase Transitions studied in the Potts model
3.1 Introduction
3.2 The surface tension in the Potts model. [GEZ50]3.3 The topology of the entropy surface S(E N) for Potts lattice gases [GV99]3.4 On the origin of isolated critical points and critical lines
Chapter 4 Liquid-gas transition and surface tension under constant pressure
4.1 Andersen’s constant pressure ensemble
4.2 Micro-canonical ensemble with given pressure; The enthalpy
4.3 Liquid-gas transition in realistic metal systems
4.4 The relation to the method of the Gibbs-ensemble
4.5 Alternative microscopic methods to calculate the surface tension
4.6 Criticism and necessary improvements of the computational method
4.7 Conclusion
Chapter 5 Statistical Fragmentation under Repulsive Forces of Long Range
5.1 Introduction
5.2 Three dimensional stress of long range : The Coulomb force
5.3 Two dimensional stress of long range: Rapidly rotating hot nuclei [BG95b]5.4 Conclusion
Chapter 6 The collapse transition in self-gravitating systems First model-studies
6.1 1 – and 2 – dim. Hamiltonian Mean Field Model a caricature of phase transitions under self-gravi
6.2 Collapse of non-extensive (gravitating) systems under conserved angular momentum
Appendix A On the historical development of statistical nuclear multifragmentation models
A.l Mathematical partition vs. quantum partition
Appendix B The micro-canonical ensemble of Na-clusters
B.1 Micro-canonical Metropolis sampling
B.2 The basic micro-canonical weights
B.3 The Metropolis pass
Appendix C Some General Technical Aspects of Microcanonical Monte Carlo Simulation on a Lattice
C.0.1 Direct sampling method:
C.0.2 2. Method using a grid of local patches c.f. fig.(C.1)
C.0.3 Using an auxiliary weight Wo(A1… AQ)
CO.4 Iterative improvement of the auxiliary weight Wo(A1…AQ)
C.l Example: The diluted Potts model

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Dieter H E Gross,Microcanonical Thermodynamics,Small Systems