2,645 research outputs found
Equilibrium fluctuation theorems compatible with anomalous response
Previously, we have derived a generalization of the canonical fluctuation
relation between heat capacity and energy fluctuations , which is able to describe the existence of macrostates with negative
heat capacities . In this work, we extend our previous results for an
equilibrium situation with several control parameters to account for the
existence of states with anomalous values in other response functions. Our
analysis leads to the derivation of three different equilibrium fluctuation
theorems: the \textit{fundamental and the complementary fluctuation theorems},
which represent the generalization of two fluctuation identities already
obtained in previous works, and the \textit{associated fluctuation theorem}, a
result that has no counterpart in the framework of Boltzmann-Gibbs
distributions. These results are applied to study the anomalous susceptibility
of a ferromagnetic system, in particular, the case of 2D Ising model.Comment: Extended version of the paper published in JSTA
Extending canonical Monte Carlo methods II
Previously, we have presented a methodology to extend canonical Monte Carlo
methods inspired on a suitable extension of the canonical fluctuation relation
compatible with negative heat capacities .
Now, we improve this methodology by introducing a better treatment of finite
size effects affecting the precision of a direct determination of the
microcanonical caloric curve , as well as
a better implementation of MC schemes. We shall show that despite the
modifications considered, the extended canonical MC methods possibility an
impressive overcome of the so-called \textit{super-critical slowing down}
observed close to the region of a temperature driven first-order phase
transition. In this case, the dependence of the decorrelation time with
the system size is reduced from an exponential growth to a weak power-law
behavior , which is shown in the particular case of
the 2D seven-state Potts model where the exponent .Comment: Version submitted to JSTA
Geometrical aspects and connections of the energy-temperature fluctuation relation
Recently, we have derived a generalization of the known canonical fluctuation
relation between heat capacity and
energy fluctuations, which can account for the existence of macrostates with
negative heat capacities . In this work, we presented a panoramic overview
of direct implications and connections of this fluctuation theorem with other
developments of statistical mechanics, such as the extension of canonical Monte
Carlo methods, the geometric formulations of fluctuation theory and the
relevance of a geometric extension of the Gibbs canonical ensemble that has
been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The
A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
In this paper the existence of a class of self-similar solutions of the
Einstein-Vlasov system is proved. The initial data for these solutions are not
smooth, with their particle density being supported in a submanifold of
codimension one. They can be thought of as intermediate between smooth
solutions of the Einstein-Vlasov system and dust. The motivation for studying
them is to obtain insights into possible violation of weak cosmic censorship by
solutions of the Einstein-Vlasov system. By assuming a suitable form of the
unknowns it is shown that the existence question can be reduced to that of the
existence of a certain type of solution of a four-dimensional system of
ordinary differential equations depending on two parameters. This solution
starts at a particular point and converges to a stationary solution
as the independent variable tends to infinity. The existence proof is based on
a shooting argument and involves relating the dynamics of solutions of the
four-dimensional system to that of solutions of certain two- and
three-dimensional systems obtained from it by limiting processes.Comment: 47 page
Classification of life by the mechanism of genome size evolution
The classification of life should be based upon the fundamental mechanism in
the evolution of life. We found that the global relationships among species
should be circular phylogeny, which is quite different from the common sense
based upon phylogenetic trees. The genealogical circles can be observed clearly
according to the analysis of protein length distributions of contemporary
species. Thus, we suggest that domains can be defined by distinguished
phylogenetic circles, which are global and stable characteristics of living
systems. The mechanism in genome size evolution has been clarified; hence main
component questions on C-value enigma can be explained. According to the
correlations and quasi-periodicity of protein length distributions, we can also
classify life into three domains.Comment: 53 pages, 9 figures, 2 table
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