20,279 research outputs found
Phase Transitions in "Small" Systems - A Challenge for Thermodynamics
Traditionally, phase transitions are defined in the thermodynamic limit only.
We propose a new formulation of equilibrium thermo-dynamics that is based
entirely on mechanics and reflects just the {\em geometry and topology} of the
N-body phase-space as function of the conserved quantities, energy, particle
number and others. This allows to define thermo-statistics {\em without the use
of the thermodynamic limit}, to apply it to ``Small'' systems as well and to
define phase transitions unambiguously also there. ``Small'' systems are
systems where the linear dimension is of the characteristic range of the
interaction between the particles. Also astrophysical systems are ``Small'' in
this sense. Boltzmann defines the entropy as the logarithm of the area
of the surface in the mechanical N-body phase space at
total energy E. The topology of S(E,N) or more precisely, of the curvature
determinant allows the classification of phase
transitions {\em without taking the thermodynamic limit}. The topology gives
further a simple and transparent definition of the {\em order parameter.}
Attention: Boltzmann's entropy S(E) as defined here is different from the
information entropy and can even be non-extensive and convex.Comment: 8 pages, 4 figures, Invited paper for CRIS200
What can nuclear collisions teach us about the boiling of water or the formation of multi-star systems ?
Phase transitions in nuclei, small atomic clusters and self-gravitating
systems demand the extension of thermo-statistics to ``Small'' systems. The
main obstacle is the thermodynamic limit. It is shown how the original
definition of the entropy by Boltzmann as the volume of the energy-manifold of
the N-body phase space allows a {\em geometrical} definition of the entropy as
function of the conserved quantities. Without invoking the thermodynamic limit
the whole ``zoo'' of phase transitions and critical points/lines can be
unambiguously defined. The relation to the Yang--Lee singularities of the
grand-canonical partition sum is pointed out. It is shown that just phase
transitions in non-extensive systems give the complete set of characteristic
parameters of the transition {\em including the surface tension.} Nuclear
heavy-ion collisions are an experimental playground to explore this extension
of thermo-statisticsComment: Invited talk for Bologna 2000, 8 pages, 3 figures.ep
Remarkable long-range-systematic in the binding energies of alpha-nuclei II
In this letter I present further data that show the remarkable evidence for
the existence of an alpha-cluster stucture in the ground states of even-even
N=Z nuclei. Such a remarkable systematic was observed 20 years ago for these
nuclei at A<= 72 and is extended here up to A=100.Comment: 3 pages, 2 figure
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