q-thermostatistics and the analytical treatment of the ideal Fermi gas

We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing statistics is derived. Special attention is paid to the mean occupation numbers of single-particle levels. Limiting instances of interest are discussed in some detail, namely, the thermodynamic limit, considering in particular both the high- and low-temperature regimes, and the approximate results pertaining to the case q \sim 1 (the conventional Fermi-Dirac statistics corresponds to q=1). We compare our findings with previous Tsallis' literature.Comment: v2: comparison with conventional results and validity of approximations clarified, typos corrected; accepted for publication in Physica

Equipartition and Virial theorems in a nonextensive optimal Lagrange multipliers scenario

We revisit some topics of classical thermostatistics from the perspective of the nonextensive optimal Lagrange multipliers (OLM), a recently introduced technique for dealing with the maximization of Tsallis' information measure. It is shown that Equipartition and Virial theorems can be reproduced by Tsallis' nonextensive formalism independently of the value of the nonextensivity index.Comment: 13 pages, no figure

Nonextensive thermodynamic relations

The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic relations for nonextensive systems. Here, taking the first law of thermodynamics and the Legendre transform structure as the basic premises, it is found that Clausius definition of the thermodynamic entropy has to be appropriately modified, and accordingly the thermodynamic relations proposed by Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be rectified. It is shown that the definition of specific heat and the equation of state remain form invariant. As an application, the classical gas model is reexamined and, in marked contrast with the previous result obtained by Abe [Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical temperature and the unphysical pressure, the specific heat and the equation of state are found to be similar to those in ordinary extensive thermodynamics.Comment: 17 pages. The discussion about the Legendre transform structure is modified and some additional comments are mad

Ideal gas in nonextensive optimal Lagrange multipliers formalism

Based on the prescription termed the optimal Lagrange multipliers formalism for extremizing the Tsallis entropy indexed by q, it is shown that key aspects of the treatment of the ideal gas problem are identical in both the nonextensive and extensive cases.Comment: 5 pages, no figure

Tsallis' entropy maximization procedure revisited

The proper way of averaging is an important question with regards to Tsallis' Thermostatistics. Three different procedures have been thus far employed in the pertinent literature. The third one, i.e., the Tsallis-Mendes-Plastino (TMP) normalization procedure, exhibits clear advantages with respect to earlier ones. In this work, we advance a distinct (from the TMP-one) way of handling the Lagrange multipliers involved in the extremization process that leads to Tsallis' statistical operator. It is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the Tsallis-Mendes-Plastino formalism.Comment: 17 pages, no figure

Thermodynamics' 0-th-Law in a nonextensive scenario

Tsallis' thermostatistics is by now recognized as a new paradigm for statistical mechanical considerations. However, it is still affected by a serious hindrance: the generalization of thermodynamics' zero-th law to a nonextensive scenario is plagued by difficulties. Here we show how to overcome this problem.Comment: 4 pages, latex; added references for section

The Reelin Pathway Modulates the Structure and Function of Retinal Synaptic Circuitry

AbstractThe formation of synaptic connections requires the coordination of specific guidance molecules and spontaneous neuronal activity. The visual system has provided a useful model for understanding the role of these cues in shaping the precise connections from the neural retina to the brain. Here, we demonstrate that two essential genes in the Reelin signaling pathway function during the patterning of synaptic connectivity in the retina. Physiological studies of mice deficient in either reelin or disabled-1 reveal an attenuation of rod-driven retinal responses. This defect is associated with a decrease in rod bipolar cell density and an abnormal distribution of processes in the inner plexiform layer . These results imply that, in addition to its essential role during neuronal migration, the Reelin pathway contributes to the formation of neuronal circuits in the central nervous system

Entropic uncertainty relation for power-law wave packets

For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the Heisenberg-type formulation, since it involves only the finite quantities. It is found that the total amount of entropic uncertainty converges to its lower bound in the limit of a large value of the exponent.Comment: 10 pages, 3 figure

A binding event converted into a folding event

AbstractWe have designed a chimeric protein by connecting a circular permutant of the α-spectrin SH3 domain to the proline-rich decapeptide APSYSPPPPP with a three-residue link. Our aim was to obtain a single-chain protein with a tertiary fold that would mimic the binding between SH3 domains and proline-rich peptides. A comparison of the circular-dichroism and fluorescence spectra of the purified chimera and the SH3 circular permutant showed that the proline-rich sequence occupies the putative SH3 binding site in a similar conformation and with comparable interactions to those found in complexes between SH3 and proline-rich peptides. Differential scanning calorimetry indicated that the interactions in the binding motif interface are highly cooperative with the rest of the structure and thus the protein unfolds in a two-state process. The chimera is more stable than the circular permutant SH3 by 6–8 kJ mol−1 at 25°C and the difference in their unfolding enthalpy is approximately 32 kJ mol−1, which coincides with the values found for the binding of proline-rich peptides to SH3 domains. This type of chimeric protein may be useful in designing SH3 peptide ligands with improved affinity and specificity

Hard photon and neutral pion production in cold nuclear matter

The production of hard photons and neutral pions in 190 MeV proton induced reactions on C, Ca, Ni, and W targets has been for the first time concurrently studied. Angular distributions and energy spectra up to the kinematical limit are discussed and the production cross-sections are presented. From the target mass dependence of the cross-sections the propagation of pions through nuclear matter is analyzed and the production mechanisms of hard photons and primordial pions are derived. It is found that the production of subthreshold particles proceeds mainly through first chance nucleon-nucleon collisions. For the most energetic particles the mass scaling evidences the effect of multiple collisions.Comment: submitted to Phys. Lett.