Dhe. Gross, MICROCANONICAL THERMODYNAMICS AND STATISTICAL FRAGMENTATION OF DISSIPATIVE SYSTEMS - THE TOPOLOGICAL-STRUCTURE OF THE N-BODY PHASE-SPACE, Physics reports, 279(3-4), 1997, pp. 120-201
This review is addressed to colleagues working in different fields of
physics who are interested in the concepts of microcanonical thermodyn
amics, its relation and contrast to ordinary, canonical or grandcanoni
cal thermodynamics, and to get a first taste of the wide area of new a
pplications of thermodynamical concepts like hot nuclei, hot atomic cl
usters and gravitating systems. Microcanonical thermodynamics describe
s how the volume of the N-body phase space depends on the globally con
served quantities like energy, angular momentum, mass, charge, etc. Du
e to these constraints the microcanonical ensemble can behave quite di
fferently from the conventional, canonical or grandcanonical ensemble
in many important physical systems. Microcanonical systems become inho
mogeneous at first-order phase transitions, or with rising energy, or
with external or internal long-range forces like Coulomb, centrifugal
or gravitational forces. Thus, fragmentation of the system into a spat
ially inhomogeneous distribution of various regions of different densi
ties and/or of different phases is a genuine characteristic of the mic
rocanonical ensemble. In these cases which are realized by the majorit
y of realistic systems in nature, the microcanonical approach is the n
atural statistical description. We investigate this most fundamental f
orm of thermodynamics in four different nontrivial physical cases:(I)
Microcanonical phase transitions of first and second order are studied
within the Potts model. The total energy per particle is a nonfluctua
ting order parameter which controls the phase which the system is in.
In contrast to the canonical form the microcanonical ensemble allows t
o tune the system continuously from one phase to the other through the
region of coexisting phases by changing the energy smoothly. The conf
igurations of coexisting phases carry important informations about the
nature of the phase transition. This is more remarkable as the canoni
cal ensemble is blind against these configurations. It is shown that t
he three basic quantities which specify a phase transition of first or
der - Transition temperature, latent heat, and interphase surface entr
opy - can be well determined for finite systems from the caloric equat
ion of state T(E) in the coexistence region. Their values are already
for a lattice of only similar to 30 30 spins close to the ones of th
e corresponding infinite system. The significance of the backbending o
f the caloric equation of state T(E) is clarified. It is the signal fo
r a phase transition of first order in a finite isolated system. (II)
Fragmentation is shown to be a specific and generic phase transition o
f finite systems. The caloric equation of state T(E) for hot nuclei is
calculated. The phase transition towards fragmentation can unambiguou
sly be identified by the anomalies in T(E). As microcanonical thermody
namics is a full N-body theory it determines all many-body correlation
s as well. Consequently, various statistical multi-fragment correlatio
ns are investigated which give insight into the details of the equilib
ration mechanism. (III) Fragmentation of neutral and multiply charged
atomic clusters is the next example of a realistic application of micr
ocanonical thermodynamics. Our simulation method, microcanonical Metro
polis Monte Carlo, combines the explicit microscopic treatment of the
fragmentational degrees of freedom with the implicit treatment of the
internal degrees of freedom of the fragments described by the experime
ntal bulk specific heat. This micro-macro approach allows us to study
the fragmentation of also larger fragments. Characteristic details of
the fission of multiply charged metal clusters find their explanation
by the different bulk properties. (IV) Finally, the fragmentation of s
trongly rotating nuclei is discussed as an example for a microcanonica
l ensemble under the action of a two-dimensional repulsive force.