182 research outputs found

### Classical Equilibrium Thermostatistics, "Sancta sanctorum of Statistical Mechanics", From Nuclei to Stars

Equilibrium statistics of Hamiltonian systems is correctly described by the
microcanonical ensemble. Classically this is the manifold of all points in the
N-body phase space with the given total energy. Due to Boltzmann-Planck's
principle, e^S=tr(\delta(E-H)), its geometrical size is related to the entropy
S(E,N,V,...). This definition does not invoke any information theory, no
thermodynamic limit, no extensivity, and no homogeneity assumption. Therefore,
it describes the equilibrium statistics of extensive as well of non-extensive
systems. Due to this fact it is the fundamental definition of any classical
equilibrium statistics. It addresses nuclei and astrophysical objects as well.
S(E,N,V,...) is multiply differentiable everywhere, even at phase-transitions.
All kind of phase transitions can be distinguished harply and uniquely for even
small systems. What is even more important, in contrast to the canonical
theory, also the region of phase-space which corresponds to phase-separation is
accessible, where the most interesting phenomena occur. No deformed q-entropy
is needed for equilibrium. Boltzmann-Planck is the only appropriate statistics
independent of whether the system is small or large, whether the system is
ruled by short or long range forces.Comment: Invited paper for NEXT2003, 10pages, 6 figures Reference 1 correcte

### Negative heat-capacity at phase-separations in microcanonical thermostatistics of macroscopic systems with either short or long-range interactions

Conventional thermo-statistics address infinite homogeneous systems within
the canonical ensemble. However, some 170 years ago the original motivation of
thermodynamics was the description of steam engines, i.e. boiling water. Its
essential physics is the separation of the gas phase from the liquid. Of
course, boiling water is inhomogeneous and as such cannot be treated by
conventional thermo-statistics. Then it is not astonishing, that a phase
transition of first order is signaled canonically by a Yang-Lee singularity.
Thus it is only treated correctly by microcanonical Boltzmann-Planck
statistics. This was elaborated in the talk presented at this conference. It
turns out that the Boltzmann-Planck statistics is much richer and gives
fundamental insight into statistical mechanics and especially into entropy.
This can be done to a far extend rigorously and analytically. The deep and
essential difference between ``extensive'' and ``intensive'' control
parameters, i.e. microcanonical and canonical statistics, was exemplified by
rotating, self-gravitating systems. In the present paper the necessary
appearance of a convex entropy $S(E)$ and the negative heat capacity at phase
separation in small as well macroscopic systems independently of the range of
the force is pointed out.Comment: 6 pages, 1 figure, 1 table; contribution to the international
conference "Next Sigma Phi" on news, expectations, and trends in statistical
physics, Crete 200

### On the inequivalence of statistical ensembles

We investigate the relation between various statistical ensembles of finite
systems. If ensembles differ at the level of fluctuations of the order
parameter, we show that the equations of states can present major differences.
A sufficient condition for this inequivalence to survive at the thermodynamical
limit is worked out. If energy consists in a kinetic and a potential part, the
microcanonical ensemble does not converge towards the canonical ensemble when
the partial heat capacities per particle fulfill the relation
$c_{k}^{-1}+c_{p}^{-1}<0$.Comment: 4 pages, 4 figure

### Non-extensive Hamiltonian systems follow Boltzmann's principle not Tsallis statistics. -- Phase Transitions, Second Law of Thermodynamics

Boltzmann's principle S(E,N,V)=k*ln W(E,N,V) relates the entropy to the
geometric area e^{S(E,N,V)} of the manifold of constant energy in the N-body
phase space. From the principle all thermodynamics and especially all phenomena
of phase transitions and critical phenomena can be deduced. The topology of the
curvature matrix C(E,N) (Hessian) of S(E,N) determines regions of pure phases,
regions of phase separation, and (multi-)critical points and lines. Thus,
C(E,N) describes all kind of phase-transitions with all their flavor. No
assumptions of extensivity, concavity of S(E), or additivity have to be
invoked. Thus Boltzmann's principle and not Tsallis statistics describes the
equilibrium properties as well the approach to equilibrium of extensive and
non-extensive Hamiltonian systems. No thermodynamic limit must be invoked.Comment: Contribution to "Non Extensive Thermodynamics and physical
applications", Villasimius, May 2001, 10 pages, 1 figur

### On the stability of the primordial closed string gas

We recast the study of a closed string gas in a toroidal container in the
physical situation in which the single string density of states is independent
of the volume because energy density is very high. This includes the gas for
the well known Brandenberger-Vafa cosmological scenario. We describe the gas in
the grandcanonical and microcanonical ensembles. In the microcanonical
description, we find a result that clearly confronts the Brandenberger-Vafa
calculation to get the specific heat of the system. The important point is that
we use the same approach to the problem but a different regularization. By the
way, we show that, in the complex temperature formalism, at the Hagedorn
singularity, the analytic structure obtained from the so-called
F-representation of the free energy coincides with the one computed using the
S-representation.Comment: 20 pages and 1 figure. The final version that appeared in JHE

### Freeze-out Configuration in Multifragmentation

The excitation energy and the nuclear density at the time of breakup are
extracted for the $\alpha + ^{197}Au$ reaction at beam energies of 1 and 3.6
GeV/nucleon. These quantities are calculated from the average relative velocity
of intermediate mass fragments (IMF) at large correlation angles as a function
of the multiplicity of IMFs using a statistical model coupled with many-body
Coulomb trajectory calculations. The Coulomb component $\vec{v}_{c}$ and
thermal component $\vec{v}_{0}$ are found to depend oppositely on the
excitation energy, IMFs multiplicity, and freeze-out density. These
dependencies allow the determination of both the volume and the mean excitation
energy at the time of breakup. It is found that the volume remained constant as
the beam energy was increased, with a breakup density of about $\rho_{0}/7$,
but that the excitation energy increased $25\%$ to about 5.5 MeV/nucleon.Comment: 12 pages, 2 figures available upon resues

### Searching for the statistically equilibrated systems formed in heavy ion collisions

Further improvements and refinements are brought to the microcanonical
multifragmentation model [Al. H. Raduta and Ad. R. Raduta, Phys. Rev. C {\bf
55}, 1344 (1997); {\it ibid.} {\bf 61}, 034611 (2000)]. The new version of the
model is tested on the recently published experimental data concerning the
Xe+Sn at 32 MeV/u and Gd+U at 36 MeV/u reactions. A remarkable good
simultaneous reproduction of fragment size observables and kinematic
observables is to be noticed. It is shown that the equilibrated source can be
unambiguously identified.Comment: Physical Review C, in pres

### Lattice gas model for fragmentation: From Argon on Scandium to Gold on Gold

The recent fragmentation data for central collisions of Gold on Gold are even
qualitatively different from those for central collisions of Argon on Scandium.
The latter can be fitted with a lattice gas model calculation. Effort is made
to understand why the model fails for Gold on Gold. The calculation suggests
that the large Coulomb interaction which is operative for the larger system is
responsible for this discrepancy. This is demonstrated by mapping the lattice
gas model to a molecular dynamics calculation for disassembly. This mapping is
quite faithful for Argon on Scandium but deviates strongly for Gold on Gold.
The molecular dynamics calculation for disassembly reproduces the
characteristics of the fragmentation data for both Gold on Gold and Argon on
Scandium.Comment: 13 pages, Revtex, 8 figures in ps files, submitted to Phys. Rev.

### The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g.
nuclei, social and financial networks, clusters, and biological systems, where
the traditional definitions of phase transitions are not applicable, is
important to obtain a deeper understanding of the phenomena observed in such
systems. Within a simple statistical model we investigate the validity and
applicability of different classification schemes for phase transtions in small
systems. We show that the whole complex temperature plane contains necessary
information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see
http://www.smallsystems.d

### Extended gaussian ensemble solution and tricritical points of a system with long-range interactions

The gaussian ensemble and its extended version theoretically play the
important role of interpolating ensembles between the microcanonical and the
canonical ensembles. Here, the thermodynamic properties yielded by the extended
gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range
interactions are analyzed. This model presents different predictions for the
first-order phase transition line according to the microcanonical and canonical
ensembles. From the EGE approach, we explicitly work out the analytical
microcanonical solution. Moreover, the general EGE solution allows one to
illustrate in details how the stable microcanonical states are continuously
recovered as the gaussian parameter $\gamma$ is increased. We found out that it
is not necessary to take the theoretically expected limit $\gamma \to \infty$
to recover the microcanonical states in the region between the canonical and
microcanonical tricritical points of the phase diagram. By analyzing the
entropy as a function of the magnetization we realize the existence of
unaccessible magnetic states as the energy is lowered, leading to a treaking of
ergodicity.Comment: 8 pages, 5 eps figures. Title modified, sections rewritten,
tricritical point calculations added. To appear in EPJ

- …