New Explanation for the Mpemba Effect
The purpose of this study is to check out the involvement of entropy in Mpemba effect. Several water samples were cooled down to frozen in order to probe if preheat affects the cooling duration time. We found out that preheating of the water sample the cooling duration was reduced. Given this, we theoretically show that water gains more entropy when warmed and re-cooled to the original temperature.
Inheritance is a Surjection: Description and Consequence
Consider an evolutionary process. In genetic inheritance and in human cultural systems each new offspring is assigned to be produced by a specific pair of the previous population. This form of mathematical arrangement is called a surjection. We have thus briefly described the mechanics of genetics – physical mechanics describes the possible forms of loci, and normal genetic statistics describe the results as viability of offspring in actual use. But we have also described much of the mechanics of mathematical anthropology. Understanding that what we know as inheritance is the result of finding surjections and their consequences, is useful in understanding, and perhaps predicting, biological, as well as human, evolution.
The New Method Using Shannon Entropy to Decide the Power Exponents on JMAK Equation
JMAK (Johnson-Mehl-Avrami-Kolmogorov) equation is exponential equation inserted power-law behavior on the parameter, which is widely utilized to describe relaxation process, nucleation process, deformation of materials and so on. Theoretically the power exponent is occasionally associated with geometrical factor of nucleus, which gives integral power exponent. However, non-integral power exponents occasionally appear and they are sometimes considered as phenomenological in the experiment. On the other hand, the power exponent decides the distribution of step-time when the equation is considered as the superposition of step function. This work intends to extend the interpretation of power exponent by the new method associating Shannon entropy of distribution of step-time with the method of Lagrange multiplier in which cumulants or moments obtained from distribution function are preserved. This method intends to decide the distribution of step-time through power exponent, in which certain statistical values are fixed. The Shannon entropy introduced the second cumulant gives fractional power exponents that reveal symmetrical distribution function that can be compared with the experimental results. Various power exponents in which other statistical value is fixed are discussed with physical interpretation. This work gives new insight into the JMAK function and the method of Shannon entropy in general.
Social Conflicts Studied by Statistical Physics Approach and Monte Carlo Simulations
Statistical physics models of social systems with a large number of members, each interacting with a subset of others, have been used in very diverse domains such as culture dynamics, crowd behavior, information dissemination and social conflicts. We observe that such models rely on the fact that large societal groups display surprising regularities despite individual agency. Unlike physics phenomena that obey Newton’s third law, in the world of humans the magnitudes of action and reaction are not necessarily equal. The effect of the actions of group n on group m can differ from the effect of group m on group n. We thus use the spin language to describe humans with this observation in mind. Note that particular individual behaviors do not survive in statistical averages. Only common characteristics remain. We have studied two-group conflicts as well as three-group conflicts. We have used time-dependent Mean-Field Theory and Monte Carlo simulations. Each group is defined by two parameters which express the intra-group strength of interaction among members and its attitude toward negotiations. The interaction with the other group is parameterized by a constant which expresses an attraction or a repulsion to other group average attitude. The model includes a social temperature T which acts on each group and quantifies the social noise. One of the most striking features is the periodic oscillation of the attitudes toward negotiation or conflict for certain ranges of parameter values. Other striking results include chaotic behavior, namely intractable, unpredictable conflict outcomes.
Spin Waves and Skyrmions in Magneto-Ferroelectric Superlattices: Theory and Simulation
We present in this paper the effects of Dzyaloshinskii-Moriya (DM) magnetoelectric coupling between ferroelectric and magnetic layers in a superlattice formed by alternate magnetic and ferroelectric films. Magnetic films are films of simple cubic lattice with Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. Electrical polarizations of 1 are assigned at simple cubic lattice sites in the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film. In zero field, the GS is periodically non collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green’s function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto-electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied.
Quantum Thermodynamics: An Introduction to the Thermodynamics of Quantum Computers
We are the verge of a technological revolution. Over the last couple of years the first computational devices have become commercially available that promise to exploit so-called quantum supremacy. Even though the thermodynamic cost for processing classical information has been known since the 1960s, the thermodynamic description of quantum computers is still at its infancy. This is due to the fact that many notions of classical thermodynamics, such as work and heat, do not readily generalize to quantum systems. In this keynote, we will outline a novel conceptual framework of an emerging theory, Quantum Thermodynamics, and illustrate its applicability, mindset, and questions with a few pedagogical examples.
Quantum Gravity Strategy for the Production of Dark Matter Using Cavitation by Minimum Entropy
The minimum entropy is responsible for the formation of dark matter bubbles in a black hole, while the variation in the density of dark matter allows these bubbles to leave the event horizon. Some experimental evidence supports the dark matter production model in the inner vicinity of the border of a black hole. The principle of Minima Entropy explains how cavitation occurs on the event horizon, which in turn complies with the Navier Stokes 3D equations. Moreover, current works in an axiomatic way show that in the event horizon Einstein's equations are equivalent to Navier Stokes' equations: "The solutions of Einstein combined with the boundary conditions we impose correspondence one-to-one with solutions of incompressible Navier-Stokes. " and "Our near-horizon limit provides a precise mathematical sense in which horizons are incompressible fluids." It is essential to understand that Cavitation by minimum entropy is the production of dark matter bubbles, by variation of the pressure inside or on the horizon of a black hole, in general Δp=p_{n+1}-p_{n}=(((σ_{n})/(σ_{n+1}))-1)p_{n} or in particular Δp=-(1-P)pā, where ((∂P)/(∂t))=((Δp)/(ρā))P. Finally, fluctuations in the density of dark matter can facilitate its escape from a black hole, if and only if there is previously dark matter produced by cavitation inside or on the horizon of a black hole and also ρ_{DM}<ρ_{B}.
Symplectic/Contact Geometry Related to Bayesian Statistics
We have the following symplectic/contact geometric description of the Bayesian inference of means: The space H of normal distributions is an upper halfplane with the two operations presenting the convolution and the normalized product of two densities. There is a diffeomorphism F of H that interchanges these operations as well as sends any e-geodesic to an e-geodesic. The product of two copies of H carries positive and negative symplectic structures and a bi-contact hypersurface N naturally generating these structures. Here the graph of F is Lagrangian with respect to the negative symplectic structure. Further, F is contained in the hypersurface N and preserved under a bi-contact flow. Then the restriction of the flow presents the inference of means. This also works for the Student t-inference of moving means and enables us to consider the smoothness of a data smoothing.
In this presentation, we will foliate the space of multivariate normal distributions by using the Cholesky decomposition of the covariance matrix to generalize the above description. Note that Hideyuki Ishi first pointed out the importance of the Cholesky decomposition in the information geometry of normal distributions. We will also construct a Lorenzian metric associated with the relative entropy. The ultimate aim of this research is to construct a relativistic space-time consisting of (tuples of) distributions, since anything can learn by changing its inner distribution in the Bayesian world view.
The increasingly sophisticated investigation of complex systems requires more robust estimates of the correlations between the measured quantities. The traditional Pearson Correlation Coefficient is easy to calculate but is sensitive only to linear correlations. The total influence between quantities is therefore often expressed in terms of the Mutual Information, which takes into account also the nonlinear effects but is not normalised. To compare data from different experiments, the Information Quality Ratio is therefore in many cases of easier interpretation. On the other hand, both Mutual Information and Information Quality Ratio are always positive and therefore cannot provide information about the sign of the influence between quantities. Moreover, they require an accurate determination of the probability distribution functions of the variables involved. Since the quality and amount of data available is not always sufficient, to grant an accurate estimation of the probability distribution functions, it has been investigated whether neural computational tools can help and complement the aforementioned indicators. Specific encoders and auto encoders have been developed for the task of determining the total correlation between quantities, including the sign of their mutual influence. Both their accuracy and computational efficiencies have been addressed in detail, with extensive numerical tests using synthetic data. The first applications to experimental databases are very encouraging.
Information Length as a New Diagnostic of Stochastic Resonance
Stochastic resonance is a subtle, yet powerful phenomenon in which a noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted a great attention with a vast number of applications in physics, chemistry, biology, etc. Popular measures to study stochastic resonance include signal-to-noise ratios, residence time distributions, and different information theoretic measures. Here, we show that the information length provides a novel method to capture stochastic resonance. The information length measures the total number of statistically different states along the path of a system. Specifically, we consider the classical double-well model of stochastic resonance in which a particle in a potential V (x, t) = [−x2/2 + x4/4 − A sin(ωt) x] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x≈ ±1. We present direct numerical solutions of the Fokker-Planck equation for the probability density function p(x, t), for ω = 10−2 to 10−6, and A ∈ [0,0.2] and show that the information length shows a veryclear signal of the resonance. That is, stochastic resonance is reflected in the total number of different statistical states that a system passes through.