Quantum boundary layer: a non-uniform density distribution of an ideal gas in thermodynamic equilibrium

Şişman, Altuğ; Öztürk, Z. Fatih; Fırat, Coşkun

doi:10.1016/j.physleta.2006.09.083

Cited by 52 publications

(62 citation statements)

References 15 publications

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“…In this case, quantum size effects (QSE) appear and considerably change the thermodynamic behavior of systems, especially near internal and external walls so that size and shape become additional parameters in the thermodynamic state function resulting in a number of effects not seen in large systems, e.g., quantum surface energy, anisotropic gas pressure, diffusion driven by size difference, quantum boundary layers, quantum forces, thermosize effects, etc. Predicting these effects constitutes a relatively new area of research (e.g., [58][59][60]) and awaits experimental verification.…”

Section: Introductionmentioning

confidence: 99%

Some Trends in Quantum Thermodynamics

Spakovsky

Gemmer

2014

Entropy

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Abstract:Traditional answers to what the 2nd Law is are well known. Some are based on the microstate of a system wandering rapidly through all accessible phase space, while others are based on the idea of a system occupying an initial multitude of states due to the inevitable imperfections of measurements that then effectively, in a coarse grained manner, grow in time (mixing). What has emerged are two somewhat less traditional approaches from which it is said that the 2nd Law emerges, namely, that of the theory of quantum open systems and that of the theory of typicality. These are the two principal approaches, which form the basis of what today has come to be called quantum thermodynamics. However, their dynamics remains strictly linear and unitary, and, as a number of recent publications have emphasized, "testing the unitary propagation of pure states alone cannot rule out a nonlinear propagation of mixtures". Thus, a non-traditional approach to capturing such a propagation would be one which complements the postulates of QM by the 2nd Law of thermodynamics, resulting in a possibly meaningful, nonlinear dynamics. An unorthodox approach, which does just that, is intrinsic quantum thermodynamics and its mathematical framework, steepest-entropy-ascent quantum thermodynamics. The latter has evolved into an effective tool for modeling the dynamics of reactive and non-reactive systems at atomistic scales. It is the usefulness of this framework in the context of quantum thermodynamics as well as the theory of typicality which are discussed here in some detail. A brief discussion of some other trends such as those related to work, work extraction, and fluctuation theorems is also presented. OPEN ACCESSEntropy 2014, 16 3435

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Section: Introductionmentioning

confidence: 99%

Some Trends in Quantum Thermodynamics

Spakovsky

Gemmer

2014

Entropy

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“…For Fermi (FD) and Bose (BE) gases, the local density obtained by using dimensionless energy eigenvalues , which are the solutions of Schrödinger equation for the LJ potential, is expressed as follows (Sisman, Ozturk, & Firat, 2007;Firat, Sisman & Ozturk, 2010;Firat & Sisman, 2009):…”

Section: Derivation Of the Density Distribution Equationsmentioning

confidence: 99%

“…All the density dependent thermodynamic properties are affected by the inhomogeneity in the density distribution (Sisman, Ozturk, & Firat, 2007;Firat, Sisman & Ozturk, 2010;Firat & Sisman, 2009).…”

Section: Introductionmentioning

confidence: 99%

Effects of Particle-Wall Interactions on the Thermodynamic Behavior of Gases at the Nano Scale

Şişman¹,

Fırat²,

Öztürk³

2011

Int. J. Thermo

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The thermodynamic behavior of gases confined in nano structures is considerably different than those in macro ones due to the effects of both particle-wall interactions and the wave character of particles. The homogeneous density distribution of a gas at thermodynamic equilibrium is disturbed by these effects. Because of particle-wall interactions, the local density of a gas changes drastically near the domain boundaries. Also, the wave character of the particles causes an inhomogeneous density distribution, especially near the boundaries. Consequently, the apparent density (number of particles over the domain volume) is different than the real one. All the densitydependent thermodynamic properties are affected by the inhomogeneity in the density distribution. Therefore, it is important to consider these effects on local density to analyze the thermodynamic behaviors of gases confined in nano structures. The detailed analysis of these effects on local density also gives a base of knowledge for the experimental verification of quantum size effects on local density due to the wave character of particles. In this study, the density distributions of classical (Maxwellian) and quantum (both Fermi and Bose) gases are calculated and investigated by considering both particle-wall interactions and quantum size effects. The results can be used for experimental verification of quantum size effects on gas density as well as the modeling of nano heat engines.

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“…It has been shown that the size effects in ideal gases cause size-dependent additional terms in the thermodynamic state functions such as the free energy. [23][24][25][26] Like the size effect, the thermosize effects of the confined quantum gas system are dependent not only on the size of the container but also the temperature. Obviously, the lower the temperature is, the longer the mean thermal wavelength of the gas and the more evident the thermosize effects of the confined gas system.…”

Section: Introductionmentioning

confidence: 99%

Thermosize Effects in Confined Quantum Gas Systems

Lin

et al. 2010

Mod. Phys. Lett. B

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Based on the grand potentials of ideal quantum gases, the number of particles, internal energy, three diagonal components of the pressure tensor, and other thermodynamic quantities of the ideal quantum gas systems confined in a rectangular box are analytically derived. It is found that the internal energy of the systems is non-extensive and that the other thermodynamic quantities, which are extensive under the thermodynamic limit condition, are also non-extensive. It is also found that the pressure tensor of the quantum gas systems in a confined space is, in general, no longer isotropic because of the geometric effect of the boundary. Moreover, the influence of the size effect of the containers on the properties of the systems and the thermosize effects in the confined quantum gas systems such as the Seebeck-like, Peltier-like and Thomson-like thermosize effects are discussed with the help of the assumption of local equilibrium. It is very significant to note that the new concept of the "mix" heat capacity, which is neither the heat capacity at constant pressure nor the heat capacity at constant volume, must be introduced in the investigation of Thomson-like thermosize effect. The results obtained may be directly used to analyze the thermodynamic properties and thermosize effects of the confined classical gas.

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Quantum boundary layer: a non-uniform density distribution of an ideal gas in thermodynamic equilibrium

Cited by 52 publications

References 15 publications

Some Trends in Quantum Thermodynamics

Some Trends in Quantum Thermodynamics

Effects of Particle-Wall Interactions on the Thermodynamic Behavior of Gases at the Nano Scale

Thermosize Effects in Confined Quantum Gas Systems

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