Abstract:
Induced abortion or the deliberate termination of pregnancy is one of the most controversial issues in legal discourse. As a legal issue, abortion is usually discussed in light of the principles of criminal law. Depending on circumstances, however, abortion can also be discussed from the standpoint of constitutional law. In the former case, the issue usually takes the form of criminalizing or decriminalizing the act, while in the latter, the issue becomes whether a pregnant woman has a constitutional right to terminate her pregnancy. The issue thus usually involves the competing arguments in favour of the “right” of the fetus to be brought onto life (i.e. personhood) vis-à-vis the right of the mother to abortion based on her interests and choice.

Abstract:
The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw [Phys. Lett. A {\bf 198} (1995) 119] has already pointed out, the concavity of Tsallis' entropy with respect to the internal energy is not sufficient to guarantee thermodynamic stability for all values of $q$ due to the non-additivity of Tsallis' entropy. Taking account of the non-additivity the differential form of the TSC for Tsallis entropy is explicitly derived. It is shown that the resultant TSC for Tsallis' entropy is equivalent to the positivity of the standard specific heat. These results are consistent with the relation between Tsallis and R\'enyi entropies.

Abstract:
The constant temperature derivation, which is a model-free derivation of the Boltzmann factor, is generalized in order to develop a new simple model-free derivation of a power-law Tsallis factor based on an environment with constant heat capacity. It is shown that the integral constant T_0 appeared in the new derivation is identified with the generalized temperature T_q in Tsallis thermostatistics. A constant heat capacity environment is proposed as a one-real-parameter extension of the Boltzmann reservoir, which is a model constant temperature environment developed by J.J. Prentis et al. [Am. J. Phys. 67 (1999) 508] in order to naturally obtain the Boltzmann factor. It is also shown that the Boltzmann entropy of such a constant heat capacity environment is consistent with Clausius' entropy.

Abstract:
For Tsallis' entropic analysis to the time evolutions of standard logistic map at the Feigenbaum critical point, it is known that there exists a unique value $q^*$ of the entropic index such that the asymptotic rate $K_q \equiv \lim_{t \to \infty} \{S_q(t)-S_q(0)\} / t$ of increase in $S_q(t)$ remains finite whereas $K_q$ vanishes (diverges) for $q > q^* (q < q^*)$. We show that in spite of the associated whole time evolution cannot be factorized into a product of independent sub-interval time evolutions, the pseudo-additive conditional entropy $S_q(t|0) \equiv \{S_q(t)-S_q(0)\}/ \{1+(1-q)S_q(0)\}$ becomes additive when $q=q^*$. The connection between $K_{q^*}$ and the rate $K'_{q^*} \equiv S_{q^*}(t | 0) / t$ of increase in the conditional entropy is discussed.

Abstract:
Stirling approximation of the factorials and multinominal coefficients are generalized based on the one-parameter ($\kappa$) deformed functions introduced by Kaniadakis [Phys. Rev. E \textbf{66} (2002) 056125]. We have obtained the relation between the $\kappa$-generalized multinominal coefficients and the $\kappa$-entropy by introducing a new $\kappa$-product operation.

Abstract:
Based on the $\kappa$-deformed functions ($\kappa$-exponential and $\kappa$-logarithm) and associated multiplication operation ($\kappa$-product) introduced by Kaniadakis (Phys. Rev. E \textbf{66} (2002) 056125), we present another one-parameter generalization of Gauss' law of error. The likelihood function in Gauss' law of error is generalized by means of the $\kappa$-product. This $\kappa$-generalized maximum likelihood principle leads to the {\it so-called} $\kappa$-Gaussian distributions.

Abstract:
in the framework of the statistical mechanics based on the sharma-taneja-mittal entropy we derive a family of nonlinear fokker-planck equations characterized by the associated non-increasing lyapunov functional. this class of equations describes kinetic processes in anomalous mediums where both super-diffusive and subdiffusive mechanisms arise contemporarily and competitively. we classify the lie symmetries and derive the corresponding group-invariant solutions for the physically meaningful uhlenbeck-ornstein process. for the purely diffusive process we show that any localized state asymptotically approaches a bell shape well fitted by a generalized gaussian which is, in general, a quasi-self-similar solution for this class of purely diffusive equations.

Abstract:
The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the $\kappa$-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the $\kappa$-Gaussian function is not a scale invariant solution of the generalized diffusive equation. Notwithstanding, several numerical simulations, with different initial conditions, show that the solutions asymptotically approach to the $\kappa$-Gaussian function. Simple argument based on a time-dependent transformation performed on the related $\kappa$-generalized Fokker-Planck equation, supports this conclusion.

Abstract:
Tsallis' thermostatistics with the standard linear average energy is revisited by employing $S_{2-q}$, which is the Tsallis entropy with $q$ replaced by $2-q$. We explore the connections among the $S_{2-q}$ approach and the other different versions of Tsallis formalisms. It is shown that the normalized $q$-average energy and the standard linear average energy are related to each other. The relations among the Lagrange multipliers of the different versions are revealed. The relevant Legendre transform structures concerning the Lagrange multipliers associated with the normalization of probability are studied. It is shown that the generalized Massieu potential associated with $S_{2-q}$ and the linear average energy is related to one associated with the normalized Tsallis entropy and the normalized $q$-average energy.

Abstract:
It is generally assumed that the thermodynamic stability of equilibrium state is reflected by the concavity of entropy. We inquire, in the microcanonical picture, on the validity of this statement for systems described by the bi-parametric entropy $S_{_{\kappa, r}}$ of Sharma-Taneja-Mittal. We analyze the ``composability'' rule for two statistically independent systems, A and B, described by the entropy $S_{_{\kappa, r}}$ with the same set of the deformed parameters. It is shown that, in spite of the concavity of the entropy, the ``composability'' rule modifies the thermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformed parameters, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})> S_{_{\kappa, r}}({\rm A})+S_{_{\kappa, r}}({\rm B})$ holds (super-additive systems), the concavity conditions does imply the thermodynamics stability. Otherwise, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})