World Scientific Lecture Notes in Physics - Vol. 66
MICROCANONICAL THERMODYNAMICS
Phase Transitions in "Small" Systems
by Dieter H E Gross (Hahn Meitner Institut, Berlin)
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.
Contents:
- The Mechanical Basis of Thermodynamics
- Micro-Canonical
Thermodynamics of Phase Transitions Studied in the Potts Model
- Liquid–Gas Transition and Surface Tension Under Constant Pressure
- Statistical Fragmentation Under Repulsive Forces of Long Range
- The Collapse Transition in Self-Gravitating Systems First Model-Studies
- Appendices:
- On the Historical Development of Statistical Nuclear Multifragmentation Models
- The Micro-Canonical Ensemble of Na-Clusters
- Some General Technical Aspects of Micro-Canonical Monte Carlo Simulation on a Lattice
Readership: Advanced level graduate students, lecturers and
researchers in statistical and condensed matter physics.
"Gross is one of the leading scientists working in the field of (multi-) fragmentation. His pre-eminence renders the book an invaluable comprehensive source for everybody who is working in the same field. For those who do not, it provides a unique, unrivalled approach to microcanonical thermodynamics, even though its scope is slightly narrower than the title might suggest. I recommend this book to researchers as well as non-experts looking for a competent guide."
| Contemporary Physics, 2003 |
| 288pp |
Pub. date: Mar 2001 |
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