Multiplicative noise: A mechanism leading to nonextensive statistical mechanics

A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point toward nonextensive statistical mechanics (based on $S_q \equiv k [1-\int du [p(u)]^q]/[q-1]$, where the value of the entropic index $q\in\Re$ depends on the specific model). We show here a family of models, with multiplicative noise, which belongs to the nonextensive class. More specifically, we consider Langevin equations of the type $\dot{u}=f(u)+g(u)\xi(t)+\eta(t)$, where $\xi(t)$ and $\eta(t)$ are independent zero-mean Gaussian white noises with respective amplitudes $M$ and $A$. This leads to the Fokker-Planck equation $\partial_t P(u,t) = -\partial_u[f(u) P(u,t)] + M\partial_u\{g(u)\partial_u[g(u)P(u,t)]\} + A\partial_{uu}P(u,t)$. Whenever the deterministic drift is proportional to the noise induced one, i.e., $f(u) =-\tau g(u) g'(u)$, the stationary solution is shown to be $P(u, \infty) \propto \bigl\{1-(1-q) \beta [g(u)]^2 \bigr\}^{\frac{1}{1-q}}$ (with $q \equiv \frac{\tau + 3M}{\tau+M}$ and $\beta=\frac{\tau+M}{2A}$). This distribution is precisely the one optimizing $S_q$ with the constraint $_q \equiv \{\int du [g(u)]^2[P(u)]^q \}/ \{\int du [P(u)]^q \}=$constant. We also introduce and discuss various characterizations of the width of the distributions.Comment: 3 PS figure

Nonextensive Entropies derived from Form Invariance of Pseudoadditivity

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of Shannon entropy. Information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity. The satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies. The proposed principle requires the same normalization as that derived in [A.K. Rajagopal and S. Abe, Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems.Comment: 16 pages, accepted for publication in Physical Review

Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg

It was recently published by M. Nauenberg [1] a quite long list of objections about the physical validity for thermal statistics of the theory sometimes referred to in the literature as {\it nonextensive statistical mechanics}. This generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the following expression for the entropy: S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv -k\sum_{i=1}^W p_i \ln p_i) . The author of [1] already presented orally the essence of his arguments in 1993 during a scientific meeting in Buenos Aires. I am replying now simultaneously to the just cited paper, as well as to the 1993 objections (essentially, the violation of "fundamental thermodynamic concepts", as stated in the Abstract of [1]).Comment: 7 pages including 2 figures. This is a reply to M. Nauenberg, Phys. Rev. E 67, 036114 (2003

Fungal diversity notes 253–366: taxonomic and phylogenetic contributions to fungal taxa

Notes on 113 fungal taxa are compiled in this paper, including 11 new genera, 89 new species, one new subspecies, three new combinations and seven reference specimens. A wide geographic and taxonomic range of fungal taxa are detailed. In the Ascomycota the new genera Angustospora (Testudinaceae), Camporesia (Xylariaceae), Clematidis, Crassiparies (Pleosporales genera incertae sedis), Farasanispora, Longiostiolum (Pleosporales genera incertae sedis), Multilocularia (Parabambusicolaceae), Neophaeocryptopus (Dothideaceae), Parameliola (Pleosporales genera incertae sedis), and Towyspora (Lentitheciaceae) are introduced. Newly introduced species are Angustospora nilensis, Aniptodera aquibella, Annulohypoxylon albidiscum, Astrocystis thailandica, Camporesia sambuci, Clematidis italica, Colletotrichum menispermi, C. quinquefoliae, Comoclathris pimpinellae, Crassiparies quadrisporus, Cytospora salicicola, Diatrype thailandica, Dothiorella rhamni, Durotheca macrostroma, Farasanispora avicenniae, Halorosellinia rhizophorae, Humicola koreana, Hypoxylon lilloi, Kirschsteiniothelia tectonae, Lindgomyces okinawaensis, Longiostiolum tectonae, Lophiostoma pseudoarmatisporum, Moelleriella phukhiaoensis, M. pongdueatensis, Mucoharknessia anthoxanthi, Multilocularia bambusae, Multiseptospora thysanolaenae, Neophaeocryptopus cytisi, Ocellularia arachchigei, O. ratnapurensis, Ochronectria thailandica, Ophiocordyceps karstii, Parameliola acaciae, P. dimocarpi, Parastagonospora cumpignensis, Pseudodidymosphaeria phlei, Polyplosphaeria thailandica, Pseudolachnella brevifusiformis, Psiloglonium macrosporum, Rhabdodiscus albodenticulatus, Rosellinia chiangmaiensis, Saccothecium rubi, Seimatosporium pseudocornii, S. pseudorosae, Sigarispora ononidis and Towyspora aestuari. New combinations are provided for Eutiarosporella dactylidis (sexual morph described and illustrated) and Pseudocamarosporium pini. Descriptions, illustrations and / or reference specimens are designated for Aposphaeria corallinolutea, Cryptovalsa ampelina, Dothiorella vidmadera, Ophiocordyceps formosana, Petrakia echinata, Phragmoporthe conformis and Pseudocamarosporium pini. The new species of Basidiomycota are Agaricus coccyginus, A. luteofibrillosus, Amanita atrobrunnea, A. digitosa, A. gleocystidiosa, A. pyriformis, A. strobilipes, Bondarzewia tibetica, Cortinarius albosericeus, C. badioflavidus, C. dentigratus, C. duboisensis, C. fragrantissimus, C. roseobasilis, C. vinaceobrunneus, C. vinaceogrisescens, C. wahkiacus, Cyanoboletus hymenoglutinosus, Fomitiporia atlantica, F. subtilissima, Ganoderma wuzhishanensis, Inonotus shoreicola, Lactifluus armeniacus, L. ramipilosus, Leccinum indoaurantiacum, Musumecia alpina, M. sardoa, Russula amethystina subp. tengii and R. wangii are introduced. Descriptions, illustrations, notes and / or reference specimens are designated for Clarkeinda trachodes, Dentocorticium ussuricum, Galzinia longibasidia, Lentinus stuppeus and Leptocorticium tenellum. The other new genera, species new combinations are Anaeromyces robustus, Neocallimastix californiae and Piromyces finnis from Neocallimastigomycota, Phytophthora estuarina, P. rhizophorae, Salispina, S. intermedia, S. lobata and S. spinosa from Oomycota, and Absidia stercoraria, Gongronella orasabula, Mortierella calciphila, Mucor caatinguensis, M. koreanus, M. merdicola and Rhizopus koreanus in Zygomycota

FREE CARRIER ABSORPTION OF RADIATION IN FERROMAGNETIC SEMICONDUCTORS

Nous avons étudié l'absorption des porteurs libres dans les semiconducteurs magnétiques. Pour satisfaire la condition de conservation de l'énergie et du moment nous avons considéré les mécanismes de diffusion suivants : phonons acoustiques, magnons et impuretés ionisées. Les résultats sont appliqués à l'interprétation des valeurs du coefficient d'absorption de EuO riche en Eu.We investigate the absorption of radiation by free carriers in ferromagnetic semiconductors. To allow energy-momentum conservation the following scattering mechanisms were considered : acoustical phonons, magnons and ionised impurities. The results are used to interpret absorption coefficient data of Eu-rich EuO

Merging Cluster Collaboration: A Panchromatic Atlas of Radio Relic Mergers

Golovich et al. present an optical imaging and spectroscopic survey of 29 radio relic merging galaxy clusters. In this paper, we study this survey to identify substructure and quantify the dynamics of the mergers. Using a combined photometric and spectroscopic approach, we identify the minimum number of substructures in each system to describe the galaxy populations and estimate the line-of-sight velocity difference between likely merging subclusters. We find that the line-of-sight velocity components of the mergers are typically small compared with the maximum 3D relative velocity (usually <1000 km s(-1) and often consistent with zero). We also compare our systems to n-body simulation analogs and estimate the viewing angle of the clean mergers in our ensemble. We find that the median system's separation vector lies within 40 degrees (17 degrees) at a 90% (50%) confidence level. This suggests that the merger axes of these systems are generally in or near the plane of the sky, matching findings in magnetohydrodynamical simulations. In 28 of the 29 systems we identify substructures in the galaxy population aligned with the radio relic(s) and presumed associated merger-induced shock. From this ensemble, we identify eight systems to include in a "gold" sample that is prime for further observation, modeling, and simulation study. Additional papers will present weak-lensing mass maps and dynamical modeling for each merging system, ultimately leading to new insight into a wide range of astrophysical phenomena at some of the largest scales in the universe