Generalized molecular chaos hypothesis and H-theorem: Problem of constraints and amendment of nonextensive statistical mechanics

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 cut-off 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.Comment: 22 pages, no figures. Accepted for publication in Phys. Rev.

Thermodynamic processes generated by a class of completely positive quantum operations

An attempt toward the operational formulation of quantum thermodynamics is made by employing the recently proposed operations forming positive operator-valued measures for generating thermodynamic processes. The quantity of heat as well as the von Neumann entropy monotonically increases under the operations. The fixed point analysis shows that repeated applications of these operations to a given system transform from its pure ground state at zero temperature to the completely random state in the high temperature limit with intermediate states being generically out of equilibrium. It is shown that the Clausius inequality can be violated along the processes, in general. A bipartite spin-1/2 system is analyzed as an explicit example.Comment: 22 pages and 1 figure. Modern Physics Letters B, in pres

Statistical quantum operation

A generic unital positive operator-valued measure (POVM), which transforms a given stationary pure state to an arbitrary statistical state with perfect decoherence, is presented. This allows one to operationally realize thermalization as a special case. The loss of information due to randomness generated by the operation is discussed by evaluating the entropy. Thermalization of the bipartite spin-1/2 system is discussed as an illustrative example.Comment: 10 pages, no figure

Temporal extensivity of Tsallis' entropy and the bound on entropy production rate

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis entropy indexed by $q$ is temporally extensive: linear growth in time, i.e., finite entropy production rate. Then, the universal bound on the entropy production rate is shown to be $1/|1-q|$ . The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.Comment: 25 pages, no figure

General relativistic effects on neutrino-driven wind from young, hot neutron star and the r-process nucleosynthesis

Neutrino-driven wind from young hot neutron star, which is formed by supernova explosion, is the most promising candidate site for r-process nucleosynthesis. We study general relativistic effects on this wind in Schwarzschild geometry in order to look for suitable conditions for a successful r-process nucleosynthesis. It is quantitatively discussed that the general relativistic effects play a significant role in increasing entropy and decreasing dynamic time scale of the neutrino-driven wind. Exploring wide parameter region which determines the expansion dynamics of the wind, we find interesting physical conditions which lead to successful r-process nucleosynthesis. The conditions which we found realize in the neutrino-driven wind with very short dynamic time scale $\tau_{\rm dyn} \sim 6$ ms and relatively low entropy $S \sim 140$. We carry out the $\alpha$-process and r-process nucleosynthesis calculation on these conditions by the use of our single network code including over 3000 isotopes, and confirm quantitatively that the second and third r-process abundance peaks are produced in the neutrino-driven wind.Comment: Accepted for publication in Ap

Entropy on the von Neumann lattice and its evaluation

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the position and momentum observables in the discrete subset of the phase space. Evaluating for a class of the coherent states, it is shown that this entropy takes a stationary value for the ground state, modulo a unit cell of the lattice in such a class. This value for the ground state depends on the ratio of the position lattice spacing and the momentum lattice spacing. It is found that its minimum is realized for the perfect square lattice, i.e., absence of squeezing. Numerical evaluation of this minimum gives 1.386....Comment: 14 pages, no figures; J. Phys. A, in pres

Baryon number segregation at the end of the cosmological quark-hadron transition

One of the most interesting questions regarding a possible first order cosmological quark--hadron phase transition concerns the final fate of the baryon number contained within the disconnected quark regions at the end of the transition. We here present a detailed investigation of the hydrodynamical evolution of an evaporating quark drop, using a multi-component fluid description to follow the mechanisms of baryon number segregation. With this approach, we are able to take account of the simultaneous effects of baryon number flux suppression at the phase interface, entropy extraction by means of particles having long mean-free-paths, and baryon number diffusion. A range of computations has been performed to investigate the permitted parameter-space and this has shown that significant baryon number concentrations, perhaps even up to densities above that of nuclear matter, represent an inevitable outcome within this scenario.Comment: 33 pages, Latex file, 6 postscript figures included in the text (psfig.tex). To appear in Phys. Rev. D1

Few-body decay and recombination in nuclear astrophysics

Three-body continuum problems are investigated for light nuclei of astrophysical relevance. We focus on three-body decays of resonances or recombination via resonances or the continuum background. The concepts of widths, decay mechanisms and dynamic evolution are discussed. We also discuss results for the triple $\alpha$ decay in connection with $2^+$ resonances and density and temperature dependence rates of recombination into light nuclei from $\alpha$-particles and neutrons.Comment: 9 pages, 8 figures. Proceedings of the 21st European Few Body Conference held in Salamanca (Spain) in August-September 201

Superstatistics, thermodynamics, and fluctuations

A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary thermodynamics is recovered as a special case of the present theory, and corrections to it can be systematically evaluated. A generalization of Einstein's relation for fluctuations is presented using a maximum entropy condition.Comment: 16 pages, no figures. The title changed, some explanations and references added. Accepted for publication in Phys. Rev.