MICROCANONICAL THERMODYNAMICS AND STATISTICAL FRAGMENTATION OF DISSIPATIVE SYSTEMS - THE TOPOLOGICAL-STRUCTURE OF THE N-BODY PHASE-SPACE

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.