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 $C=\beta^{2}$ compatible with negative heat capacities $C<0$. 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 $\beta (E) =\partial S(E) /\partial E$, 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 $\tau$ with the system size $N$ is reduced from an exponential growth to a weak power-law behavior $\tau(N)\propto N^{\alpha}$, which is shown in the particular case of the 2D seven-state Potts model where the exponent $\alpha=0.14-0.18$.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 $k_{B}C=\beta^{2}$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. 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

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

Understanding critical behavior in the framework of the extended equilibrium fluctuation theorem

Recently (arXiv:0910.2870), we have derived a fluctuation theorem for systems in thermodynamic equilibrium compatible with anomalous response functions, e.g. the existence of states with \textit{negative heat capacities} $C<0$. In this work, we show that the present approach of the fluctuation theory introduces new insights in the understanding of \textit{critical phenomena}. Specifically, the new theorem predicts that the environmental influence can radically affect critical behavior of systems, e.g. to provoke a suppression of the divergence of correlation length $\xi$ and some of its associated phenomena as spontaneous symmetry breaking. Our analysis reveals that while response functions and state equations are \emph{intrinsic properties} for a given system, critical behaviors are always \emph{relative phenomena}, that is, their existence crucially depend on the underlying environmental influence