A Definition of Metastability for Markov Processes with Detailed Balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach \cite{pen71}. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.Comment: 5 pp. 1 Figure, presented in News, Expectations and Trends in Statistical Physics-3rd International Conference, 13-18 August 2005, Kolymbari Cret

Exact order, gap and counting statistics of a Brownian gas correlated by resetting

We study a one-dimensional gas of $N$ Brownian particles that diffuse independently, but are simultaneously reset to the origin at a constant rate $r$. The system approaches a non-equilibrium stationary state (NESS) with long-range interactions induced by the simultaneous resetting. Despite the presence of strong correlations, we show that several observables can be computed exactly, which include the global average density, the distribution of the position of the rightmost particle, the spacing distribution between two successive particles and the full counting statistics, i.e., the distribution of the number of particles in a given interval. Our analytical results are confirmed by numerical simulations. We also discuss a possible experimental realisation of this resetting gas using optical traps.Comment: 6 pages + 7 pages (Supplementary Material), 2 figure

Data from: Multiple scaling behavior and nonlinear traits in music scores

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear auto-correlations by estimating the detrended fluctuation analysis of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece

InfoSeries.jl-master

Repository for every calculation of the DFA and the construction of the time series from the .csv file. The repository can also be consulted in GitHub: https://github.com/spiralizing/InfoSeries.j

SI-master

Supporting Information, here are the graphs for the fluctuation functions. The graphs are labeled as following: Palestrina Motets: PalestrinaMo-# Bach Musical Offering: BachMO-# Bach Well Tempered Clavier: BachWTK-# Haydn String Quartets: HaydnSQ-# Mozart Piano Sonatas: MozartPS-# Mozart String Quartets: MozartSQ-# Beethoven Fugues: BeethovenF-# Beethoven Early Quartets: BeethovenEQ-# Beethoven Late Quartets: BeethovenLQ-# Dvorak Humoresques: DvorakH-# Dvorak Silhouettes: DvorakS-# Dvorak Serenade for Strings: DvorakSt-# Shostakovich Preludes and Fugues: ShostakovichPF-# The number corresponds to the place in the full list of opus. Files corresponding to a scaling behavior over all s boxes (profile 1) are in Scaling.pdf, files corresponding to the functions showing a crossover (profiles 1 and 2) are in Crossovers.pdf, the files with the graps of profiles 4 and 5 are in NoScaling.pdf The values of the alpha's and R squared for the linear fitting in the fluctuations function are on the Tables: TableScaling.pdf corresponds to the functions following a power law and TableCrossovers.pdf to the functions with a crossover