Searcharxiv⌕ Search

arXiv subjects

Takuya Yamano

Publications and source records attributed to Takuya Yamano.

13 recordsLinked to original sources
arXiv2013

Phase space gradient of dissipated work and information: A role of relative Fisher information

We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated work in phase space. We present a universal constraint on it via the logarithmic Sobolev inequality. Furthermore, we point out that a possible expression of the lower bound indicates a deep connection in terms of the relative entropy and the Fisher information of the canonical distributions.

cond-mat.stat-mech↗
arXiv2013

de Bruijn-type identity for systems with flux

We show that an information-theoretic relation called the de Bruijn-type identity can be reformulated in a physical context with probability currents. The time derivatives of relative entropies under the continuity equation are presented, which shows that the conservation of distance between a pair of distributions is generally not guaranteed. As an important implication of these results, we discuss and present a possible conceptual framework for the classical no-cloning (deleting) theorem and qualitatively assert that we can attribute the perfect performance of the operating machine to the openness (non-vanishing flow at boundaries between the processing machine and the system) during the process.

cond-mat.stat-mech↗
arXiv2013

Fluctuation of gauge field for general nonlinear Fokker-Planck equation and covariant version of Fisher information matrix

We clarify a strong link between general nonlinear Fokker-Planck equations with gauge fields associated with nonequilibrium dynamics and the Fisher information of the system. The notion of Abelian gauge theory for the non-equilibrium Fokker-Planck equation has proposed in the literature, in which the associated curvature represents internal geometry. We present the fluctuation of the gauge field can be decomposed into three parts. We further show that if we define the Fisher information matrix by using a covariant derivative then it gives correlation of the flux components but it is not gauge invariant.

cond-mat.stat-mech↗
arXiv2012

Bounds for Fisher information and its production under flow

We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in presence of a flux vector, which satisfies the continuity equation. We also establish a novel upper bound on the time derivative (production) in terms of the arrow of time and derive a lower bound by the logarithmic Sobolev inequality. These serve as the revealing dynamics of the information content and its limitations pertaining to nonequilibrium processes.

cond-mat.stat-mech↗
arXiv2009

A generalization of the Kullback-Leibler divergence and its properties

A generalized Kullback-Leibler relative entropy is introduced starting with the symmetric Jackson derivative of the generalized overlap between two probability distributions. The generalization retains much of the structure possessed by the original formulation. We present the fundamental properties including positivity, metricity, concavity, bounds and stability. In addition, a connection to shift information and behavior under Liouville dynamics are discussed.

cond-mat.stat-mech↗
arXiv2006

Stylized Facts in Internal Rates of Return on Stock Index and its Derivative Transactions

Universal features in stock markets and their derivative markets are studied by means of probability distributions in internal rates of return on buy and sell transaction pairs. Unlike the stylized facts in log normalized returns, the probability distributions for such single asset encounters encorporate the time factor by means of the internal rate of return defined as the continuous compound interest. Resulting stylized facts are shown in the probability distributions derived from the daily series of TOPIX, S & P 500 and FTSE 100 index close values. The application of the above analysis to minute-tick data of NIKKEI 225 and its futures market, respectively, reveals an interesting diffference in the behavior of the two probability distributions, in case a threshold on the minimal duration of the long position is imposed. It is therefore suggested that the probability distributions of the internal rates of return could be used for causality mining between the underlying and derivative stock markets. The highly specific discrete spectrum, which results from noise trader strategies as opposed to the smooth distributions observed for fundamentalist strategies in single encounter transactions may be also useful in deducing the type of investment strategy from trading revenues of small portfolio investors.

cs.IT↗
arXiv2005

Some formal properties on superstatistics and superposition of statistical factors

By focusing on the interchangeable role in a generating function (i.e., $β\leftrightarrow E$ in the Laplace transform), the superstatistics proposed by Beck and Cohen can be viewed as a counterpart of the canonical partition function. Some formal properties of this superstatistics are presented in connection with thermodynamic structures and information aspects. For any combination of the local equilibrium statistical factor and the form of fluctuating field, which are ingredients of making a generic superstatistics, a variance of the fluctuating quantity appears in the correction term. This fact enables us to relate parameters contained in the statistical factor with the variance in {\it any} situation.

cond-mat.stat-mech↗
arXiv2004

Nonadditive statistical measure of complexity and values of the entropic index q

A two-parameter family of statistical measures of complexity are introduced based on the Tsallis-type nonadditive entropies. This provides a unified framework for the study of the recently proposed various measures of complexity as well as for the discussion of a whole new class of measures. As a special case, a generalization of the measure proposed by Landsberg and his co-workers based on the Tsallis entropy indexed by q is discussed in detail and its behavior is illustrated using the logistic map. The value of the entropic index, q, with which the maximum of the measure of complexity is located at the edge of chaos, is calculated.

cond-mat.stat-mech↗
arXiv2001

Regulation effects on market with Bak-Sneppen model in high dimensions

We present the effect of regulations on self-organized market by using biological model of Bak-Sneppen in higher dimensions. This study extends the idea of Cuniberti et.al. The higher-dimensional description of the market suffices less effect of regulation than that of lower one.

cond-mat.stat-mech↗
arXiv2001

Generalized symmetric mutual information applied for the channel capacity

The channel capacity for the binary symmetric channel is investigated based on the symmetrized definition of the mutual information, which is arising from an attempt of extension of information content based on the nonadditivity. The negative capacity can emerge as an avoidable consequence for the generalization of the concept of the information entropy when $q >1$.

cond-mat.stat-mech↗
arXiv2001

Information Theory based on Non-additive Information Content

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity $q$ and the codeword length is pointed out.

cond-mat.stat-mech↗
arXiv2000

On the robust thermodynamical structures against arbitrary entropy form and energy mean value

We discuss that the thermodynamical Legendre transform structure can be retained not only for the arbitrary entropic form but also for the arbitrary form of the energy constraints by following the discussion of Plastino and Plastino. The thermodynamic relation between the expectation values and the conjugate Lagrange multipliers are seen to be universal. Furthermore, Gibbs' fundamental equation is shown to be unaffected by the choice of the entropy and the definition of the mean values due to the robustness of the Legendre transform structure.

cond-mat.stat-mech↗