Phase diagram and reentrance for the 3D Edwards–Anderson model using information theory

Quantifying Hidden Order out of Equilibrium

“…More recently, application to statistical physics has been mostly through the analysis of the time dependence of single-site variables. For equilibrium systems, a time series of the spin or the Edwards-Anderson autocorrelation parameter at a given site, obtained by Monte Carlo simulation, was used to locate the critical points of the 3D Edwards-Anderson spin glass [17] and the 2D and 3D Ising models [18,19], and to approximate the entropy of the 2D Ising model [19]. Data compression has also proven to be a useful tool in the definition and characterization of complexity of (mostly one-dimensional) dynamical models, such as cellular automata and dynamical systems [20][21][22][23][24][25][26], as well as for turbulence [27].…”

Information theory as a tool to improve individual pensions: The Chilean case

“…Very recently a new tool has been introduced to analyze the fluctuations of assets over any period τ : this is the mutability µ(τ ) obtained by means of information theory [8,6]. The method arose from phase transitions in physics where agitation of a gas or individual magnetic orientations can be characterized in this way [8,10]. In short what is done is the following: (i) consider the file storing the evolution of the asset v(t) at regular intervals t within the range [0, τ ]; (ii) obtain the computer memory occupancy or weight in bytes w(v(τ )) of this file; (iii) compress the file storing v(t) in the interval [0, τ ] and designate by w * (v(τ )) the weight of the compressed file; then the mutability µ(v(τ )) is given by the ratio of the weight of the compressed file over the weight of the original file, namely:…”

“…The idea comes from the physics of magnetic phase transitions where the transit from a ferromagnetic phase to a paramagnetic phase is preceded by fluctuations in any order parameter (magnetization, site order parameter, correlations) as temperature raises [7,8]. Something similar has been found for the ferromagnetic to spin-glass transition [9,10]. The technique is based on the generation of a time series that is recorded as a vector in a file.…”

“…An additional goal is to apply the method of information theory that has been successful in other fields [9,7,8,10] to the case of pensions based on personal investments; we will show the advantages that can be obtained from the use of this information.…”

Measuring the seismic risk along the Nazca-Southamerican subduction front: Shannon entropy and mutability

“…A entropy could be defined in natural time by S ≡ χln(χ) − χ ln χ , and has been very useful in the analysis of global seismicity (Rundle et al, 2019). Bressan et al (Bressan et al, 2017) On the other hand, the method based on information theory (Luenberg, 2006;Cover et al, 2006;Roederer 2005) was introduced a decade ago when it was successfully used to detect phase transitions in magnetism (Vogel et al, 2009;Vogel el al., 2012;Cortez et al, 2014). Then a new data compressor was designed to recognize compatible data, namely, data based on specific properties of the system.…”