A New Approach for the Statistical Thermodynamic Theory of the Nonextensive Systems Confined in Different Finite Traps

Tang, Hui-yi; Wang, Jianhui; Ma, Yongli

doi:10.7566/jpsj.83.064004

Cited by 5 publications

(9 citation statements)

References 83 publications

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“…We only need to deal with the coupling between the finite systems with the infinite heat bath since the super reservoir coupled to the entire system is not needed [29]. Both in the previous works [1,2] and in the present paper, the coupling between the system and the infinite heat bath is just the thermodynamic coupling.…”

mentioning

confidence: 91%

“…This δS for the process to achieve thermal equilibrium has been related to fluctuation theorems [37][38][39][40]. The numerical works have shown [1,2] T cl > T and E > E eq . This suggests that the process is just the irreversible process.…”

mentioning

confidence: 95%

“…We have introduced the generalized BGSF which has an invariance form in all thermodynamic process. The total thermal energy E is proportional to T and the equilibrium entropy as a function of (N , V, T ) is obtained [1,2]. But we did not compared the effects of coupling between the system and infinite heat bath with the experimental specific heats and entropies.…”

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confidence: 99%

“…Although the individual specific heats of the combined system plus bath and the bare bath can never be negative according to the CE theory, their difference can be negative at the low T of the small systems. In our previous papers [1,2] we have constructed the fundamental statistical theory for the nonextensive systems without and with the interacting between particles. We have introduced the generalized BGSF which has an invariance form in all thermodynamic process.…”

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confidence: 99%

“…The generalized BGSF, the entropy expression for S eq (N , V, T ), and total thermal energy equation E = E(N , V, T ) are derived based on the fundamental thermodynamical laws [1,2]. In studying the finite system within the exact MCE [18], the temperature T is is obtained by…”

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confidence: 99%

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Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics

Zhou

Tang

2014

J Low Temp Phys

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Based on a new statistical theory, we investigate the thermodynamic anomalies of small quantum systems, such as the negative specific heat (NSH) and negative entropy (NE) within the generalized canonical ensemble. We consider the systembath heat exchange and "uncompensated heat" in the thermodynamical level which is independent on the details of the system-bath coupling. For ideal finite systems, we calculate two thermodynamic quantities, i.e., the experimental specific heat and the entropy. The results show that the NSH and NE exist in quantum thermodynamics, particularly at low temperatures for small systems. They agree with the results of the reduced partition function theory and reveal that the finite boundary effects of the uncompensated heat and heat exchange of small quantum systems dominate the nonequilibrium irreversible processes. Keywords Small quantum system · Negative specific heat · Negative entropy Thermodynamics and the traditional statistical-mechanical interpretation are originally developed for large systems in the equilibrium state. However, the theories are not sufficient to describe the thermodynamical properties of small quantum systems [1-3]. There are increasing findings of anomalies presented experimentally in these systems [4][5][6][7][8][9]. These experimental results [6,10,11] turn up the existence of negative specific heat (NSH) and negative entropy (NE) [12]. But the specific heat is necessarily positive both in the standard Boltzmann-Gibbs statistical theories of the canonical ensemble (CE) and grand-canonical ensemble (GCE) and in the exact CE theory on the

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confidence: 91%

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confidence: 95%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics

Zhou

Tang

2014

J Low Temp Phys

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Asynchronous finite differences in most probable distribution with finite numbers of particles

Liu

2022

Annals of Physics

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Temperature based Restricted Boltzmann Machines

Deng

et al. 2016

Sci Rep

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Restricted Boltzmann machines (RBMs), which apply graphical models to learning probability distribution over a set of inputs, have attracted much attention recently since being proposed as building blocks of multi-layer learning systems called deep belief networks (DBNs). Note that temperature is a key factor of the Boltzmann distribution that RBMs originate from. However, none of existing schemes have considered the impact of temperature in the graphical model of DBNs. In this work, we propose temperature based restricted Boltzmann machines (TRBMs) which reveals that temperature is an essential parameter controlling the selectivity of the firing neurons in the hidden layers. We theoretically prove that the effect of temperature can be adjusted by setting the parameter of the sharpness of the logistic function in the proposed TRBMs. The performance of RBMs can be improved by adjusting the temperature parameter of TRBMs. This work provides a comprehensive insights into the deep belief networks and deep learning architectures from a physical point of view.

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A New Approach for the Statistical Thermodynamic Theory of the Nonextensive Systems Confined in Different Finite Traps

Cited by 5 publications

References 83 publications

Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics

Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics

Asynchronous finite differences in most probable distribution with finite numbers of particles

Temperature based Restricted Boltzmann Machines

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