Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to... more Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated H-theorem, whereas the q-average widely used in the relevant literature is not. In the course of the analysis, the distributions with finite cutoff factors are rigorously treated. Accordingly, the formulation of nonextensive statistical mechanics is amended based on the normal average. In addition, the Shore-Johnson theorem, which supports the use of the q-average, is carefully reexamined, and it is found that one of the axioms may not be appropriate for systems to be treated within the framework of nonextensive statistical mechanics.
Physica A: Statistical Mechanics and its Applications, 2008
Stationary photon-atom entanglement is discussed by applying the method of flow equation to the J... more Stationary photon-atom entanglement is discussed by applying the method of flow equation to the Jaynes-Cummings model. A nonlocal continuous unitary transformation is explicitly constructed and the associated positive operator-valued measures for the photons and atom are obtained. Then, flow of the entanglement entropy is analyzed. A comment is also made on implementing the unitary operation in the method of flow equation. This method may offer a new strategy for quantum-state engineering.
Physica A: Statistical Mechanics and its Applications, 2011
Earthquake network is known to be of the small-world type. The values of the network characterist... more Earthquake network is known to be of the small-world type. The values of the network characteristics, however, depend not only on the cell size (i.e., the scale of coarse graining needed for constructing the network) but also on the size of a seismic data set. Here, discovery of a scaling law for the clustering coefficient in terms of the data size, which is refereed to here as finite data-size scaling, is reported. Its universality is shown to be supported by the detailed analysis of the data taken from California, Japan and Iran. Effects of setting threshold of magnitude are also discussed.
An explicit form of a generic unital quantum operation, which transforms a given stationary pure ... more An explicit form of a generic unital quantum operation, which transforms a given stationary pure state to an arbitrary statistical state with perfect decoherence, is presented. This allows one to operationally realize the thermal state as a special case. The loss of information due to randomness generated by the operation is discussed by evaluating the entropy. Realization of the thermal state of a bipartite spin-1/2 system is discussed as an illustrative example.
Journal of Statistical Mechanics: Theory and Experiment, 2009
A generalized definition of average, termed the q-average, is widely employed in the field of non... more A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific deformations of probability distributions. Here, the following three issues are discussed and clarified. Firstly, the deformations considered are physical and may experimentally be realized. Secondly, in view of thermostatistics, the q-average is unstable in both finite and infinite discrete systems. Thirdly, a naive generalization of the discussion to continuous systems misses a point, and a norm better than the L 1-norm should be employed for measuring the distance between two probability distributions. Consequently, stability of the q-average is shown not to be established in all the cases.
Journal of Statistical Mechanics: Theory and Experiment, 2008
In a recent work, Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) have shown by using the ... more In a recent work, Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) have shown by using the properties of Hamiltonian dynamics and a statistical mechanical consideration that, through contact, heat exchange between two systems initially prepared at different temperatures obeys a fluctuation theorem. Here, another proof is presented, in which only macroscopic thermodynamic quantities are employed. The detailed balance condition is found to play an essential role. As a result, the theorem is found to hold under very general conditions.
It is shown by simple and straightforward considerations that discreteness of basic physical vari... more It is shown by simple and straightforward considerations that discreteness of basic physical variables is, at least, essential for generalized statistical mechanics with nonlogarithmic entropy to be thermodynamically applicable to classical systems. As a result, continuous Hamiltonian systems with long-range interactions and the so-called q-Gaussian momentum distributions are seen to be outside the scope of nonextensive statistical mechanics.
The properties of earthquake networks have been studied so far mainly for the seismic data sets t... more The properties of earthquake networks have been studied so far mainly for the seismic data sets taken from California, Japan and Iran, and features common in these regions have been reported in the literature. Here, an earthquake network is constructed and analyzed for the Chilean data to examine if the scale-free and small-world properties of the earthquake networks constructed in the other geographical regions can also be found in seismicity in Chile. It is shown that the result is affirmative: in all the regions both the exponent γ of the power-law connectivity distribution and the clustering coefficient C take the universal invariant values γ ≈ 1 and , respectively, as the cell size becomes larger than a certain value, which is the scale of coarse graining needed for constructing earthquake network. An interpretation for this remarkable result is presented based on physical considerations.
Physica A: Statistical Mechanics and its Applications, 2009
The scaling relation derived by Dorogovtsev, Goltsev, Mendes and Samukhin [Phys. Rev. E, 68 (2003... more The scaling relation derived by Dorogovtsev, Goltsev, Mendes and Samukhin [Phys. Rev. E, 68 (2003) 046109] states that the exponents of the power-law connectivity distribution, γ , and the power-law eigenvalue distribution of the adjacency matrix, δ , of a locally treelike scale-free network satisfy 2γ − δ = 1 in the mean field approximation. Here, it is shown that this relation holds well for the reduced simple earthquake networks (without tadpole-loops and multiple edges) constructed from the seismic data taken from California and Japan. The result is interpreted from the viewpoint of the hierarchical organization of the earthquake networks.
Distant regional cross correlations are analyzed for seismicity in Japan by making use of the the... more Distant regional cross correlations are analyzed for seismicity in Japan by making use of the theory of random matrices as the null hypothesis. The empirical correlation matrix is shown to strongly deviate from the random matrix of the Wishart type. Accordingly, nonuniversal (i.e., nonrandom) correlations are identified and are represented by the networks on the map of Japan. The effect of setting threshold for magnitude is also examined, and it is found that the threshodling alters the results only slightly.
q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. ... more q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. Here, it is shown that the q-expectation value is not stable under small deformations of a probability distribution function, in general, whereas the ordinary expectation value is always stable.
Nonequilibrium complex systems are often effectively described by the mixture of different dynami... more Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent theoretical framework for such a description. Here, a theory is developed for log-normal superstatistics based on the fluctuation theorem for entropy changes as well as the maximum entropy method. This gives novel physical insight into log-normal statistics, other than the traditional multiplicative random processes. A comment is made on a possible application of the theory to the fluctuating energy dissipation rate in turbulence.
In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and Meister have shown by ... more In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through the changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal independently of any of the parameters contained in the model.
Generalizing a recent work [T. Taniguchi and E. G. D. Cohen, J. Stat. Phys. 126, 1 (2006)] that w... more Generalizing a recent work [T. Taniguchi and E. G. D. Cohen, J. Stat. Phys. 126, 1 (2006)] that was based on the Onsager-Machlup theory, a nonlinear relaxation process is considered for a macroscopic thermodynamic quantity. It is found that the fluctuation theorem holds in the nonlinear nonequilibrium regime if the change of the entropy characterized by local equilibria is appropriately renormalized. The fluctuation theorem for the ordinary entropy change is recovered in the linear near-equilibrium case. This result suggests a possibility that the information-theoretic entropy of the Shannon form may be modified in the strongly nonlinear nonequilibrium regime.
Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to... more Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated H-theorem, whereas the q-average widely used in the relevant literature is not. In the course of the analysis, the distributions with finite cutoff factors are rigorously treated. Accordingly, the formulation of nonextensive statistical mechanics is amended based on the normal average. In addition, the Shore-Johnson theorem, which supports the use of the q-average, is carefully reexamined, and it is found that one of the axioms may not be appropriate for systems to be treated within the framework of nonextensive statistical mechanics.
Physica A: Statistical Mechanics and its Applications, 2008
Stationary photon-atom entanglement is discussed by applying the method of flow equation to the J... more Stationary photon-atom entanglement is discussed by applying the method of flow equation to the Jaynes-Cummings model. A nonlocal continuous unitary transformation is explicitly constructed and the associated positive operator-valued measures for the photons and atom are obtained. Then, flow of the entanglement entropy is analyzed. A comment is also made on implementing the unitary operation in the method of flow equation. This method may offer a new strategy for quantum-state engineering.
Physica A: Statistical Mechanics and its Applications, 2011
Earthquake network is known to be of the small-world type. The values of the network characterist... more Earthquake network is known to be of the small-world type. The values of the network characteristics, however, depend not only on the cell size (i.e., the scale of coarse graining needed for constructing the network) but also on the size of a seismic data set. Here, discovery of a scaling law for the clustering coefficient in terms of the data size, which is refereed to here as finite data-size scaling, is reported. Its universality is shown to be supported by the detailed analysis of the data taken from California, Japan and Iran. Effects of setting threshold of magnitude are also discussed.
An explicit form of a generic unital quantum operation, which transforms a given stationary pure ... more An explicit form of a generic unital quantum operation, which transforms a given stationary pure state to an arbitrary statistical state with perfect decoherence, is presented. This allows one to operationally realize the thermal state as a special case. The loss of information due to randomness generated by the operation is discussed by evaluating the entropy. Realization of the thermal state of a bipartite spin-1/2 system is discussed as an illustrative example.
Journal of Statistical Mechanics: Theory and Experiment, 2009
A generalized definition of average, termed the q-average, is widely employed in the field of non... more A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific deformations of probability distributions. Here, the following three issues are discussed and clarified. Firstly, the deformations considered are physical and may experimentally be realized. Secondly, in view of thermostatistics, the q-average is unstable in both finite and infinite discrete systems. Thirdly, a naive generalization of the discussion to continuous systems misses a point, and a norm better than the L 1-norm should be employed for measuring the distance between two probability distributions. Consequently, stability of the q-average is shown not to be established in all the cases.
Journal of Statistical Mechanics: Theory and Experiment, 2008
In a recent work, Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) have shown by using the ... more In a recent work, Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) have shown by using the properties of Hamiltonian dynamics and a statistical mechanical consideration that, through contact, heat exchange between two systems initially prepared at different temperatures obeys a fluctuation theorem. Here, another proof is presented, in which only macroscopic thermodynamic quantities are employed. The detailed balance condition is found to play an essential role. As a result, the theorem is found to hold under very general conditions.
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