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[en] A deduction of generalized quantum entropies within the Tsallis and Kaniadakis frameworks is derived using a generalization of the ordinary multinomial coefficient. This generalization is based on the respective deformed multiplication and division. We show that the two above entropies are consistent with ones arbitrarily assumed at other contexts. -- Highlights: → Derivation of generalized quantum entropies. → Generalized combinatorial method. → Non-Gaussian quantum statistics.
[en] Members in a social group may change over time: a new member is recruited; a current member stops his or her position; a candidate supersedes a member of the group. Here we investigate the effects of changes of nodes on the dynamics of opinion formation. In our model, opinion formation is in two stages. In the first stage, a network evolves through a voting process that is used to select agents to add into the network, to remove from the network or to be replaced by other agents. Special rules for the voting process are necessary in the first stage. We focus on two rules, namely, majority rule and random rule. In the second stage, opinion formation takes place. We find that the majority rule generally foster consensus formation in comparison to the random rule. We also investigate the effects of changes of agents on two-party systems, in which there are two parties and opinions of members in the same party are close to each other. In particular, the effects of diversity of opinions for two-party systems are studied. A counterintuitive finding is that the diversity of opinions, instead of hindering consensus formation, facilitates consensus formation. (paper: classical statistical mechanics, equilibrium and non-equilibrium)
[en] Gibbs paradox statement of entropy of mixing has been regarded as the theoretical foundation of statistical mechanics, quantum theory and biophysics. However, all the relevant chemical experimental observations and logical analyses indicate that the Gibbs paradox statement is false. I prove that this statement is wrong: Gibbs paradox statement implies that entropy decreases with the increase in symmetry (as represented by a symmetry number σ; see any statistical mechanics textbook). From group theory any system has at least a symmetry number σ=1 which is the identity operation for a strictly asymmetric system. It follows that the entropy of a system is equal to, or less than, zero. However, from either von Neumann-Shannon entropy formula (S(w) =-Σω in p1) or the Boltzmann entropy formula (S = in w) and the original definition, entropy is non-negative. Therefore, this statement is false. It should not be a surprise that for the first time, many outstanding problems such as the validity of Pauling's resonance theory, the explanation of second order phase transition phenomena, the biophysical problem of protein folding and the related hydrophobic effect, etc., can be solved. Empirical principles such as Pauli principle (and Hund's rule) and HSAB principle, etc., can also be given a theoretical explanation
[en] By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner consistent with the thermostatistics structure of the theory. We show that the definitions of these quantities are sensitive to the composition law of entropy and internal energy governing the system. In this way, we can clarify some questions raised about the possible introduction of intensive variables in the context of non-extensive statistical mechanics.
[en] In this note an attempt is presented to show that: a) an operative analysis of the concept of distinguishability of identical particles leads to the conclusion that it is not applicable to the statistical description of a physical system; statistical thermodynamics would then require the concept of indistinguishability; b) by its own the concept of indistinguishability will require, when the Planck constant is properly introduced in the deductive analysis, the uncertainty correlation relation ΔqΔp>=h. (Author)
[en] The workshop and satellite conference held in July 2013 at the Kavli Institute for Theoretical Physics China (KITPC) of the Chinese Academy of Sciences (CAS) brought together experts of a variety of different fields, and constituted a unique opportunity to share ideas and breed new ones in a strongly interdisciplinary fashion. At the same time, the breadth of the scope of these two meetings was so wide that the need for a collection of reference books and papers was pointed out, in order to help the interested professionals, as well as graduate students, both to tackle the technically advanced issues and to bridge the gaps, necessarily present in each other's background. Therefore, we invited some of the participants to produce a bibliography containing the most relevant works in their own fields, and to complement this bibliography with a short explanation of the content of those books and papers. We are thus very grateful to Igor Goychuk, David Lacoste, Annick Lesne, Andrea Puglisi, Hong Qian and Hugo Touchette for having accepted our invitation and for having produced what we consider a very useful tool for all those who want to learn or to understand more deeply the current theories concerning small and nonequilibrium systems. (interdisciplinary physics and related areas of science and technology)
[en] The present paper deals with the investigation of the conjugated equation for the generating function in a particular case
[fr]Dans ce papier on recherche l'equation conjuguee de la fonction generative dans un cas particulier
[en] A large deviation function mathematically characterizes the statistical property of atypical events. In recent years, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the fluctuation theorem. Despite such significance, large deviation functions have not been easily obtained in laboratory experiments. Thus, in order to understand the physical significance of large deviation functions, it is necessary to consider their experimental measurability in greater detail. This aspect of large deviation is discussed with the presentation of a future problem.
[en] We study some aspects of the equilibrium statistical mechanics of a classical two-dimensional one-component Coulomb plasma (the interaction is logarithmic). The free energy is calculated exactly, for one special value of the temperature. At low temperature, the particles form a triangular lattice, which is stable; its vibration modes are well-behaved longitudinal plasmons and transverse phonons. The self-consistent harmonic approximation is studied; it has a solution for the transverse sound velocity at low temperature only, a strong indication that the solid phase is unstable at high temperature. The free energies obtained in different ways are compared. It is very likely that the model has a solid-fluid phase transition
[en] In this paper we present a classification of the extreme events – very small and very large outcomes – of positive-valued random variables. The classification distinguishes five different categories of randomness, ranging from the very ‘mild’ to the very ‘wild’. In analogy with the common five-tone musical scale we term the classification ‘pentatonic’. The classification is based on the analysis of the inherent Gibbsian ‘forces’ and ‘temperatures’ existing on the logarithmic scale of the random variables under consideration, and provides a statistical-physics insight regarding the nature of these random variables. The practical application of the pentatonic classification is remarkably straightforward, it can be performed by non-experts, and it is demonstrated via an array of examples