Non-extensive thermodynamics of transition-metal nanoclusters☆

Hasegawa, Hideo

doi:10.1016/j.pmatsci.2006.10.006

Cited by 10 publications

(9 citation statements)

References 61 publications

(81 reference statements)

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“…Although (c) normalized MEM [30] with the q-average was adopted in our previous papers [55-58,79], we have employed in the present study, (a) original MEM with the normal average [28,73]. In Appendix A, thermodynamical quantities of the entropy, specific heat and susceptibility calculated by (a) original MEM [28,73] with the normal average are summarized and compared to the previous ones obtained by (c) normalized MEM [30] with the q-average [55][56][57][58]79]. In Appendix B the NES with (a) original MEM [28,73] is applied also to Heisenberg dimers.…”

Section: Maximum-entropy Methods In the Nesmentioning

confidence: 99%

Thermal entanglement of Hubbard dimers in the nonextensive statistics

Hasegawa¹

2011

Physica A: Statistical Mechanics and its Applications

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The thermal entanglement of the Hubbard dimer (two-site Hubbard model) has been studied with the nonextensive statistics. We have calculated the auto-correlation ($O_q$), pair correlation ($L_q$), concurrence ($\Gamma_q$) and conditional entropy ($R_q$) as functions of entropic index $q$ and the temperature $T$. The thermal entanglement is shown to considerably depend on the entropic index. For $q < 1.0$, the threshold temperature where $\Gamma_q$ vanishes or $R_q$ changes its sign is more increased and the entanglement may survive at higher temperatures than for $q=1.0$. Relations among $L_q$, $\Gamma_q$ and $R_q$ are investigated. The physical meaning of the entropic index $q$ is discussed with the microcanonical and superstatistical approaches. The nonextensive statistics is applied also to Heisenberg dimers.Comment: 28 pages, 6 figures; the final version accepted in Physica

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Section: Maximum-entropy Methods In the Nesmentioning

confidence: 99%

Thermal entanglement of Hubbard dimers in the nonextensive statistics

Hasegawa¹

2011

Physica A: Statistical Mechanics and its Applications

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“…The Boltzmann distribution function, as mentioned above, provides a valid approximation only under certain assumptions for equilibrium thermodynamic [25,39,40]. While it allows a relatively accurate description of macroscopic systems in which a very large number of stochastic events take place, when one goes to smaller scales for instance, such a description breaks down [41].…”

Section: The Generalized Boltzmann Factormentioning

confidence: 99%

On the Gouy-Chapman-Stern model of the electrical double-layer structure with a generalized Boltzmann factor

Allagui,

Benaoum,

Olendski

2022

Preprint

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The classical treatment of the electrical double-layer (EDL) structure at a planar metal/electrolyte junction via the Gouy-Chapman-Stern (GCS) approach is based on the Poisson equation relating the electrostatic potential to the net mean charge density. The ions concentration in the diffuse layer are assumed to follow the Boltzmann distribution law, i.e. ∝ exp(− ψ) where ψ is the dimensionless electrostatic potential. However, even in stationary equilibrium in which variables are averaged over a large number of elementary stochastic events, deviations from the mean-value are expected. In this study we evaluate the behavior of the EDL by assuming some small perturbations superposed on top of its Boltzmann distribution of ion concentrations using the Tsallis nonextensive statistics framework. With this we assume the ion concentrations to be proportional to [1 − (1 − q) ψ] 1/(1−q) = exp q (− ψ) with q being a real parameter that characterizes the system's statistics. We derive analytical expression and provide computational results for the overall differential capacitance of the EDL structure, which, depending on the values of the parameter q can show both the traditional inverse bell-shaped curves for aqueous solutions and bell curves observed with ionic liquids.

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“…Small systems are ideal components for these uses because they present very high surface to volume ratios [1], but the consequences of the OPEN ACCESS progress in small system design and synthesis have pointed out the importance of scale-related properties, often different from the macroscopic ones [2].…”

Section: Introductionmentioning

confidence: 99%

A Link between Nano- and Classical Thermodynamics: Dissipation Analysis (The Entropy Generation Approach in Nano-Thermodynamics)

Lucia

2015

Entropy

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Abstract:The interest in designing nanosystems is continuously growing. Engineers apply a great number of optimization methods to design macroscopic systems. If these methods could be introduced into the design of small systems, a great improvement in nanotechnologies could be achieved. To do so, however, it is necessary to extend classical thermodynamic analysis to small systems, but irreversibility is also present in small systems, as the Loschmidt paradox highlighted. Here, the use of the recent improvement of the Gouy-Stodola theorem to complex systems (GSGL approach), based on the use of entropy generation, is suggested to obtain the extension of classical thermodynamics to nanothermodynamics. The result is a new approach to nanosystems which avoids the difficulties highlighted in the usual analysis of the small systems, such as the definition of temperature for nanosystems.

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Non-extensive thermodynamics of transition-metal nanoclusters☆

Cited by 10 publications

References 61 publications

Thermal entanglement of Hubbard dimers in the nonextensive statistics

Thermal entanglement of Hubbard dimers in the nonextensive statistics

On the Gouy-Chapman-Stern model of the electrical double-layer structure with a generalized Boltzmann factor

A Link between Nano- and Classical Thermodynamics: Dissipation Analysis (The Entropy Generation Approach in Nano-Thermodynamics)

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