2,448 research outputs found

### Some thoughts on theoretical physics

Some thoughts are presented on the inter-relation between beauty and truth in
science in general and theoretical physics in particular. Some conjectural
procedures that can be used to create new ideas, concepts and results are
illustrated in both Boltzmann-Gibbs and nonextensive statistical mechanics. The
sociological components of scientific progress and its unavoidable and benefic
controversies are, mainly through existing literary texts, briefly addressed as
well.Comment: Short essay based on the plenary talk given at the International
Workshop on Trends and Perspectives in Extensive and Non-Extensive
Statistical Mechanics, held in November 19-21, 2003, in Angra dos Reis,
Brazil. To appear in a Physica A special volume (2004) edited by E.M.F.
Curado, H.J. Herrmann and M. Barbosa. 23 pages, including 3 figures. The new
version has 25 pages and the same figures. The texts by Saramago and by
Bersanelli are now translated into English. A few typos and minor
improvements are included as wel

### Negative specific heat in a Lennard-Jones-like gas with long-range interactions

We study, through molecular dynamics, a conservative two-dimensional
Lennard-Jones-like gas (with attractive potential $\propto r^{-\alpha}$). We
consider the effect of the range index $\alpha$ of interactions, number of
particles, total energy and particle density. We detect negative specific heat
when the interactions become long-ranged ($0\le \alpha/d<1$).Comment: LaTeX, 8 pages, 4 eps figures, contributed paper to the Proceedings
of the International School and Workshop on Nonextensive Thermodynamics and
physical applications, NEXT 2001, 23-30 May 2001, Cagliari (Italy) (Physica
A) (New Title, new Fig. 4

### Dynamical scenario for nonextensive statistical mechanics

Statistical mechanics can only be ultimately justified in terms of
microscopic dynamics (classical, quantum, relativistic, or any other). It is
known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential
sensitivity to the initial conditions, mixing and ergodicity in Gibbs
$\Gamma$-space. What are the corresponding hypothesis for nonextensive
statistical mechanics? A scenario for answering such question is advanced,
which naturally includes the {\it a priori} determination of the entropic index
$q$, as well as its cause and manifestations, for say many-body Hamiltonian
systems, in (i) sensitivity to the initial conditions in Gibbs $\Gamma$-space,
(ii) relaxation of macroscopic quantities towards their values in anomalous
stationary states that differ from the usual thermal equilibrium (e.g., in some
classes of metastable or quasi-stationary states), and (iii) energy
distribution in the $\Gamma$-space for the same anomalous stationary states.Comment: Invited paper at the Second Sardinian International Conference on
"News and Expectations in Thermostatistics" held in Villasimius (Cagliari)-
Italy in 21-28 September 2003. 12 pages including 2 figure

### Equipartition and Virial theorems in a nonextensive optimal Lagrange multipliers scenario

We revisit some topics of classical thermostatistics from the perspective of
the nonextensive optimal Lagrange multipliers (OLM), a recently introduced
technique for dealing with the maximization of Tsallis' information measure. It
is shown that Equipartition and Virial theorems can be reproduced by Tsallis'
nonextensive formalism independently of the value of the nonextensivity index.Comment: 13 pages, no figure

### Generalized thermostatistics based on deformed exponential and logarithmic functions

The equipartition theorem states that inverse temperature equals the
log-derivative of the density of states. This relation can be generalized by
introducing a proportionality factor involving an increasing positive function
phi(x). It is shown that this assumption leads to an equilibrium distribution
of the Boltzmann-Gibbs form with the exponential function replaced by a
deformed exponential function. In this way one obtains a formalism of
generalized thermostatistics introduced previously by the author. It is shown
that Tsallis' thermostatistics, with a slight modification, is the most obvious
example of this formalism and corresponds with the choice phi(x)=x^q.Comment: Invited talk at Next2003, uses Elsevier LaTeX macro

### Dynamical anomalies and the role of initial conditions in the HMF model

We discuss the role of the initial conditions for the dynamical anomalies
observed in the quasi-stationary states of the Hamiltonian Mean Field (HMF)
model.Comment: 8 pages, 5 figures, submitted to Physica A for the proceedings of the
conference Frontier Science 2003 Pavia, Italy, 8-12 September 200

### Low temperature specific heat of glasses: a non-extensive approach

Specific heat is calculated using Tsallis statistics. It is observed that it
is possible to explain some low temperature specific heat properties of glasses
using non-extensive approach. A similarity between temperature dependence of
non-extensive specific heat and fractal specific heat is also discussed.Comment: 5 pages, 4 figure

### Generalized Simulated Annealing

We propose a new stochastic algorithm (generalized simulated annealing) for
computationally finding the global minimum of a given (not necessarily convex)
energy/cost function defined in a continuous D-dimensional space. This
algorithm recovers, as particular cases, the so called classical ("Boltzmann
machine") and fast ("Cauchy machine") simulated annealings, and can be quicker
than both. Key-words: simulated annealing; nonconvex optimization; gradient
descent; generalized statistical mechanics.Comment: 13 pages, latex, 4 figures available upon request with the authors

### Nonuniqueness of Canonical Ensemble Theory arising from Microcanonical Basis

Given physical systems, counting rule for their statistical mechanical
descriptions need not be unique, in general. It is shown that this
nonuniqueness leads to the existence of various canonical ensemble theories
which equally arise from the definite microcanonical basis. Thus, the Gibbs
theorem for canonical ensemble theory is not universal, and the maximum entropy
principle is to be appropriately modefied for each physical context.Comment: 13 pages; This is a thoroughly revised version of the original
preprint which has now appearted in print. It also corrects several errors
and misstatements in the published version. The main conclusions of the paper
however remain intac

### Is the entropy Sq extensive or nonextensive?

The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics
respectively are the entropies $S_{BG} \equiv -k \sum_{i=1}^W p_i \ln p_i$ and
$S_{q}\equiv k (1-\sum_{i=1}^Wp_i^{q})/(q-1) (q\in{\mathbb R} ; S_1=S_{BG})$.
Through them we revisit the concept of additivity, and illustrate the (not
always clearly perceived) fact that (thermodynamical) extensivity has a well
defined sense {\it only} if we specify the composition law that is being
assumed for the subsystems (say $A$ and $B$). If the composition law is {\it
not} explicitly indicated, it is {\it tacitly} assumed that $A$ and $B$ are
{\it statistically independent}. In this case, it immediately follows that
$S_{BG}(A+B)= S_{BG}(A)+S_{BG}(B)$, hence extensive, whereas
$S_q(A+B)/k=[S_q(A)/k]+[S_q(B)/k]+(1-q)[S_q(A)/k][S_q(B)/k]$, hence
nonextensive for $q \ne 1$. In the present paper we illustrate the remarkable
changes that occur when $A$ and $B$ are {\it specially correlated}. Indeed, we
show that, in such case, $S_q(A+B)=S_q(A)+S_q(B)$ for the appropriate value of
$q$ (hence extensive), whereas $S_{BG}(A+B) \ne S_{BG}(A)+S_{BG}(B)$ (hence
nonextensive).Comment: To appear in the Proceedings of the 31st Workshop of the
International School of Solid State Physics ``Complexity, Metastability and
Nonextensivity", held at the Ettore Majorana Foundation and Centre for
Scientific Culture, Erice (Sicily) in 20-26 July 2004, eds. C. Beck, A.
Rapisarda and C. Tsallis (World Scientific, Singapore, 2005). 10 pages
including 1 figur

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