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As known, a method to introduce non-conventional statistics may be realized by modifying the number of possible combinations to put particles in a collection of single-particle states. In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain analytical function $f_{\left\{\pi \right\}}\left(n\right)$ of the actual number of particles present in every energy level. Following this approach, the configurational Boltzmann entropy is revisited in a very general manner starting from a continuous deformation of the multinomial coefficients depending on a set of deformation parameters $\left\{\pi \right\}$. It is shown that, when $f_{\left\{\pi \right\}}\left(n\right)$ is related to the solutions of a simple linear difference–differential equation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree $(\kappa ,r)$ known, in the framework of the information theory, as Sharma–Taneja–Mittal entropic form. Full article

The cubic intermetallic compound Sm${}_3$Co${}_4$Ge${}_{13}$ (space group $Pm\overline{3}n$ ) possesses a cage-like structure composed of Ge and displays an antiferromagnetic transition at $T_N\approx$ 6 K in magnetization, $M\left(T\right)$ , specific heat, $C_p\left(T\right)$ and in thermal conductivity, $\kappa \left(T\right)$. The magnetic transition at $T_N$ is observed to be robust against applied magnetic fields up to 9 T. From the analysis of specific heat, a Sommerfeld coefficient $\gamma$ = 80(2) mJ/mol-Sm K${}^2$ is estimated. The magnetic entropy released at $T_N$ is estimated as lower than that of a doublet, R ln(2). A positive Seebeck coefficient is observed for the thermopower, $S\left(T\right)$. Photoemission spectroscopy reveals distinct electronic character of the near-$E_{\mathrm{F}}$ valence band states arising out of Co($3d$)-Sm($4f$) hybridization and Sm($4f$) electron correlation. The unusual field-independent features in magnetization, specific heat and electrical transport is an indication of the significant correlation between f and d wave functions. Full article

In this study, we analyze the role of the thermoelectric (TE) properties, namely Seebeck coefficient α, thermal conductivity κ and electrical resistivity ρ, of three different materials in a composite thermoelectric generator (CTEG) under different configurations. The CTEG is composed of three thermoelectric modules (TEMs): (1) two TEMs thermally and electrically connected in series (SC); (2) two branches of TEMs thermally and electrically connected in parallel (PSC); and (3) three TEMs thermally and electrically connected in parallel (TEP). In general, each of the TEMs have different thermoelectric parameters, namely a Seebeck coefficient α, a thermal conductance K and an electrical resistance R. Following the framework proposed recently, we show the effect of: (1) the configuration; and (2) the arrangements of TE materials on the corresponding equivalent figure of merit Z_eq and consequently on the maximum power P_max and efficiency η of the CTEG. Firstly, we consider that the whole system is formed of the same thermoelectric material (α1,K1,R1 = α2,K2,R2 = α3,K3,R3) and, secondly, that the whole system is constituted by only two different thermoelectric materials Entropy 2015, 17 7388 (α_i,K_i,R_i ≠ αj ,K_j ,R_j 6= α_l,K_l,R_l, where i, j, l can be 1, 2 or 3). In this work, we propose arrangements of TEMs, which clearly have the advantage of a higher thermoelectric figure of merit value compared to a conventional thermoelectric module. A corollary about the Z_eq-max for CTEG is obtained as a result of these considerations. We suggest an optimum configuration. Full article