Dark Information in Black Hole with λφ Fluid

It has been shown that the nonthermal spectrum of Hawking radiation will lead to information-carrying correlations between emitted particles in the radiation. The mutual information carried by such correlations can not be locally observed and hence is dark. With dark information, the black hole information is conserved. In this paper, we look for the spherically symmetric black hole solution in a λφ fluid model and investigate the radiation spectrum and dark information of the black hole. The spacetime structure of this black hole is similar to that of the Schwarzschild one, while its horizon radius is decreased by the λφ fluid. By using the statistical mechanical method, the nonthermal radiation spectrum is calculated. This radiation spectrum is very different from the Schwarzschild case at its last stage because of the effect of the λφ fluid. The λφ fluid reduces the lifetime of the black hole, but increases the dark information of the Hawking radiation.

Review of Sublinear Modeling in Probabilistic Graphical Models by Statistical Mechanical Informatics and Statistical Machine Learning Theory

We review sublinear modeling in probabilistic graphical models by statistical mechanical informatics and statistical machine learning theory. Our statistical mechanical informatics schemes are based on advanced mean-field methods including loopy belief propagations. This chapter explores how phase transitions appear in loopy belief propagations for prior probabilistic graphical models. The frameworks are mainly explained for loopy belief propagations in the Ising model which is one of the elementary versions of probabilistic graphical models. We also expand the schemes to quantum statistical machine learning theory. Our framework can provide us with sublinear modeling based on the momentum space renormalization group methods.

Statistical-mechanical analysis of adaptive filter with clipping saturation-type nonlinearity

Adaptive signal processing is used in broad areas. In most practical adaptive systems, there exists substantial nonlinearity that cannot be neglected. In this paper, we analyze the behaviors of an adaptive system in which the output of the adaptive filter has the clipping saturation-type nonlinearity by a statistical-mechanical method. To represent the macroscopic state of the system, we introduce two macroscopic variables. By considering the limit in which the number of taps of the unknown system and adaptive filter is large, we derive the simultaneous differential equations that describe the system behaviors in the deterministic and closed form. Although the derived simultaneous differential equations cannot be analytically solved, we discuss the dynamical behaviors and steady state of the adaptive system by asymptotic analysis, steady-state analysis, and numerical calculation. As a result, it becomes clear that the saturation value S has the critical value SC at which the mean-square stability of the adaptive system is lost. That is, when S > SC, both the mean-square error (MSE) and mean-square deviation (MSD) converge, i.e., the adaptive system is mean-square stable. On the other hand, when S < SC, the MSD diverges although the MSE converges, i.e., the adaptive system is not mean-square stable. In the latter case, the converged value of the MSE is a quadratic function of S and does not depend on the step size. Finally, SC is exactly derived by asymptotic analysis.<br>

Statistical-mechanical analysis of adaptive filter with clipping saturation-type nonlinearity

Adaptive signal processing is used in broad areas. In most practical adaptive systems, there exists substantial nonlinearity that cannot be neglected. In this paper, we analyze the behaviors of an adaptive system in which the output of the adaptive filter has the clipping saturation-type nonlinearity by a statistical-mechanical method. To represent the macroscopic state of the system, we introduce two macroscopic variables. By considering the limit in which the number of taps of the unknown system and adaptive filter is large, we derive the simultaneous differential equations that describe the system behaviors in the deterministic and closed form. Although the derived simultaneous differential equations cannot be analytically solved, we discuss the dynamical behaviors and steady state of the adaptive system by asymptotic analysis, steady-state analysis, and numerical calculation. As a result, it becomes clear that the saturation value S has the critical value SC at which the mean-square stability of the adaptive system is lost. That is, when S > SC, both the mean-square error (MSE) and mean-square deviation (MSD) converge, i.e., the adaptive system is mean-square stable. On the other hand, when S < SC, the MSD diverges although the MSE converges, i.e., the adaptive system is not mean-square stable. In the latter case, the converged value of the MSE is a quadratic function of S and does not depend on the step size. Finally, SC is exactly derived by asymptotic analysis.<br>

Understanding entropy

A new way of understanding entropy as a macroscopic property is presented. This is based on the fact that heat flows from a hot body to a cold one even when the hot one is smaller and has less energy. A quantity that determines the direction of flow is shown to be the increment of heat gained (q) divided by the absolute temperature (T). The same quantity is shown to determine the direction of other processes taking place in isolated systems provided that q is determined by the state (s) of the system. Entropy emerges as the potent energy of a system [Σ(qs/T)], the potency being determined by 1/T. This is shown to tie in with the statistical mechanical interpretation of entropy. The treatment is shorter than the traditional one based on heat engines.

Phenomenological Tsallis distribution from thermal field theory

Classical and quantum Tsallis distributions have been widely used in many branches of natural and social sciences. But, the quantum field theory of the Tsallis distributions is relatively a less explored arena. In this paper, we derive the expression for the thermal two-point functions in the Tsallis statistics with the help of the corresponding statistical mechanical formulations. We show that the quantum Tsallis distributions used in the literature appear in the thermal part of the propagator much in the same way the Boltzmann–Gibbs distributions appear in the conventional thermal field theory. As an application of our findings, we calculate the thermal mass in the [Formula: see text] scalar field theory within the realm of the Tsallis statistics.