Traditional Statistical Physics Research Articles

Emergence of biological complexity: Criticality, renewal and memory

The key purpose of this article is to establish a connection between two emerging fields of research in theoretical biology. The former focuses on the concept of criticality borrowed from physics that is expected to be extensible to biology through a robust theoretical approach that although not yet available shall eventually shed light into the origin of cognition. The latter, largely based on the tracking of single molecules diffusing in biological cells, is bringing to the general attention the need to go beyond the ergodic assumption currently done in the traditional statistical physics. We show that replacing critical slowing down with temporal complexity explains why biological systems at criticality are resilient and why long-range correlations are compatible with the free-will condition necessary for the emergence of cognition. Temporal complexity generates ergodicity breakdown and requires new forms of response of complex systems to external stimuli. We concisely illustrate these new forms of information transport and we also address the challenging issue of combining temporal complexity with coherence and renewal with infinite memory.

Thermodynamic properties of Fermi gas under generalized uncertainty principle

When taking into account the generalized uncertainty principle in statistical physics, the density of states must make a correction, which causes all the results of traditional statistical physics to have different degrees of correction. In high-energy or high-temperature conditions, this amendment can subvert the traditional concept and there are also some certain amendments at low temperatures. In this paper we study the thermodynamic properties of the ideal and weakly interacting Fermi gas in low temperature conditions when the generalized uncertainty principle is taken into account. Firstly, analytical expressions of chemical potential, internal energy and heat capacity at constant volume of ideal or weakly interacting Fermi gas are given. Then the properties of copper electron gas are computed as an example, showing that when the generalized uncertainty principle is taken into account the chemical potential, Fermi energy and the ground state energy increase with the increase of temperature, while the heat capacity decreases. When the temperature is lower than 0.3 times TF0, the internal energy increases with the increase of temperature, but becomes decreased when temperature is high than 0.3 times TF0. These amendments are mostly dependent on particle density, which becomes bigger and bigger with particle density increasing.

Incomplete <i>E-V</i> Distribution for Shannon Entropy

Within the framework of nonextensive and incomplete statistical physics, we derive theE-Vdistribution (the extent is alterable) which is based on the deformed Shannon entropy, and discuss the revision for the traditional statistical physics (BGS) with deformed parameterq>1 andq<1 respectively, taking linear filament as an example.

Exact Partition Function Zeros of the Wako-Saitô-Muñoz-Eaton Protein Model

Protein is an intrinsically finite size system with heterogeneous components, which is in contrast to infinite-size homogeneous systems studied in traditional statistical physics, and it is of interest to see to what extent methodologies of statistical physics can be used for studying protein folding. Partition function zeros(PFZs) method is a tool used in statistical physics for studying phase transition, where instead of computing quantities in real temperature, the zeros of the partition function in the complex temperature plane are examined. In this work, I show that the PFZs method can be used for distinguishing two-state and barrierless downhill folding transitions, by computing exact partition function zeros of the Wako-Saito-Munoz-Eaton protein model. I compute the PFZs for various secondary structural elements, and for two proteins 1BBL and 1I6C, which exhibit features that clearly distinguish distinct types of folding transitions. The result is expected to form basis for further application of the method to finite heterogeneous systems.Physical Review Letters 110 (2013) 248101.

A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling

Because classical music has greatly affected our life and culture in its long history, it has attracted extensive attention from researchers to understand laws behind it. Based on statistical physics, here we use a different method to investigate classical music, namely, by analyzing cumulative distribution functions (CDFs) and autocorrelation functions of pitch fluctuations in compositions. We analyze 1,876 compositions of five representative classical music composers across 164 years from Bach, to Mozart, to Beethoven, to Mendelsohn, and to Chopin. We report that the biggest pitch fluctuations of a composer gradually increase as time evolves from Bach time to Mendelsohn/Chopin time. In particular, for the compositions of a composer, the positive and negative tails of a CDF of pitch fluctuations are distributed not only in power laws (with the scale-free property), but also in symmetry (namely, the probability of a treble following a bass and that of a bass following a treble are basically the same for each composer). The power-law exponent decreases as time elapses. Further, we also calculate the autocorrelation function of the pitch fluctuation. The autocorrelation function shows a power-law distribution for each composer. Especially, the power-law exponents vary with the composers, indicating their different levels of long-range correlation of notes. This work not only suggests a way to understand and develop music from a viewpoint of statistical physics, but also enriches the realm of traditional statistical physics by analyzing music.

Anomaly-based detection using synergetic neural network

Network traffic anomaly detection has become a popular research tendency, as it can detect new type attacks in real time. However, the network traffic appears as a complex dynamic system, causing by the collaboration of many network factors. Although various methods have been proposed to detect anomalies, they are mostly based on the traditional statistical physics. In these methods, all factors are integrated to analyze the variation of the network traffic. But in fact, the changing trend of the network traffic at some moment is only determined by a few primary factors. This paper presents a non-statistical network traffic anomaly detection method based on the synergetic neural networks. In our method, a synergetic dynamic equation based on the order parameters is used to describe the complex behavior of the network traffic system. When the synergetic dynamic equation is evolved, only the order parameter determined by the primary factors can converge to 1. Therefore, the network traffic anomaly can be detected by referring to the primary factors. We evaluate our approach using the intrusion evaluation data set of the network traffic provided by the defense advanced research projects agency (DARPA). Experiment results show that our approach can effectively detect the network anomaly and achieve high detection probability and low false alarms rate.

Diagram technique for finding of vertex functions in the Landau theory of heteropolymer liquids

The problem on finding the coefficients of the Landau free energy expansion into the power series of parameter of order has been considered for solutions and melts of linear heteropolymers whose molecules comprise several types monomeric units arranged stochastically. The presence of such a quenched structural disorder places this problem outside the framework of the traditional statistical physics inviting for its solution special approaches. One of them, based on the replica concept and actively engaged in theoretical physics of disordered systems, has been invoked in this paper to derive expressions for the vertex functions in the Landau theory of heteropolymer liquids. An algorithm has been formulated which permits one resorting to the simple diagram technique to write down expressions for these functions of any order in terms of the statistical characteristics of chemical quenched structure of polymer molecules. Explicit expressions for the contributions to the Landau free energy up to the fourth degree of order parameters for polymer systems with an arbitrary structural disorder have been presented to illustrate this general algorithm. Its potentialities have been also exemplified for the melt of random m-component copolymer where exact analytical formulas for these contributions up to n=6 at an arbitrary m have been derived for the first time.

Ergodic property of a Henon-Heiles model with reflecting walls.

A modified Henon-Heiles model with reflecting walls is suggested to discuss the ergodic property of the motion of a two-dimensional oscillator with nonlinear coupling. A quantitative method for estimating the ergodicity of a chaotic trajectory is proposed in terms of a microcanonical distribution. The influence of the boundary on the ergodic and chaotic behavior is discussed. Our investigations show that, by adjusting the distance and the shape of the boundary, a simple Henon-Heiles system can reach ergodicity on the constant-energy surface, and therefore various concepts in traditional statistical physics can be introduced into this simple system.