Foundation of Equilibrium Statistical Mechanics Based on Generalized Entropy

Parvan, A.S.

doi:10.5772/60997

Cited by 4 publications

(7 citation statements)

References 17 publications

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“…Thus, we have obtained that if the thermodynamic potential is a homogeneous function of the first order and the temperature is intensive, then the thermodynamic potential is an additive function and the potential inhomogeneity is zero. This proves the zeroth law of thermodynamics for the grand canonical ensemble [29,30].…”

Section: Thermodynamic Potential and Zeroth Law Of Thermodynamicssupporting

confidence: 66%

“…To prove the zeroth law of thermodynamics, let us divide the system into two subsystems (1 and 2). Then the extensive variables of state of the grand canonical ensemble should be additive and the intensive variables of state should be the same [29,30]…”

Section: Thermodynamic Potential and Zeroth Law Of Thermodynamicsmentioning

confidence: 99%

“…Let us consider the case when the thermodynamic potential of the grand canonical ensemble is indeed a homogeneous function of the first order with respect to the extensive variable of state V . We have [29,30] Ω(T, V, µ) = V ω(T, µ).…”

Section: Thermodynamic Potential and Zeroth Law Of Thermodynamicsmentioning

confidence: 99%

“…The formalism of statistical mechanics agrees with the zeroth law of thermodynamics under the condition that the thermodynamic potential of the statistical ensemble, which contains all information about the physical system, is a homogeneous function of the first order with respect to the extensive variables of state [25][26][27][28][29][30]. For most physical systems this condition is fulfilled in the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

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Finite size effects in the thermodynamics of a free neutral scalar field

Parvan

2018

Physica A: Statistical Mechanics and its Applications

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The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.

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Section: Thermodynamic Potential and Zeroth Law Of Thermodynamicssupporting

confidence: 66%

Section: Thermodynamic Potential and Zeroth Law Of Thermodynamicsmentioning

confidence: 99%

Section: Thermodynamic Potential and Zeroth Law Of Thermodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite size effects in the thermodynamics of a free neutral scalar field

Parvan

2018

Physica A: Statistical Mechanics and its Applications

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“…The main purpose of this study is to find the analytical expression for the transverse momentum distribution of the Tsallis statistics [15], which was developed in [23,24,22,25], in the case of the ultrarelativistic Maxwell-Boltzmann particles and demonstrate that the momentum distribution of the Tsallis-factorized statistics [7,8] in the case of massless particles corresponds to the zeroth term approximation of the Tsallis statistics with transformation of the parameter q to parameter 1/q c . Note that the thermodynamic self-consistency of the Tsallis statistics [15] in the different statistical ensembles was demonstrated in [23,24,22,25]. The thermodynamic self-consistency of the Tsallis-factorized statistics was proved in [7,8].…”

Section: Introductionmentioning

confidence: 99%

Ultrarelativistic transverse momentum distribution of the Tsallis statistics

Parvan¹

2017

Eur. Phys. J. A

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Abstract. The analytical expressions for the ultrarelativistic transverse momentum distributions of the Tsallis and the Tsallis-2 statistics were obtained. We found that the transverse momentum distribution of the Tsallis-factorized statistics, which is now largely used to describe the experimental transverse momentum spectra of hadrons measured in pp collisions at LHC and RHIC energies, in the ultrarelativistic case is not equivalent to the transverse momentum distributions of the Tsallis and the Tsallis-2 statistics. However, we revealed that this distribution exactly coincides with the transverse momentum distribution of the Tsallis-2 statistics in the zeroth term approximation and is transformed to the transverse momentum distribution of the Tsallis statistics in the zeroth term approximation by changing the parameter q to 1/qc. We demonstrated analytically on the basis of the ultrarelativistic ideal gas that the Tsallis-factorized statistics is not equivalent to the Tsallis and the Tsallis-2 statistics. In the present paper the Tsallis statistics corresponds to the standard expectation values.PACS. 13.85.-t Hadron-induced high-and super-high-energy interactions -13.85.Hd Inelastic scattering: many-particle final states -24.60.-k Statistical theory and fluctuations

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The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies

Anghel¹,

Parvan²

2018

J. Phys. A: Math. Theor.

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The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is maximized at equilibrium. We say that the macroscopic systems are extensive and so it is also the entropy. For a mesoscopic system, by definition, the size and the contacts with other systems influence its thermodynamic properties and therefore, if we define an entropy, this cannot be a homogeneous of order one function in the extensive variables.So, mesoscopic systems and their entropies are non-extensive. While for macroscopic systems and homogeneous entropies the equilibrium conditions are clearly defined, it is not so clear how the nonextensive entropies should be applied for the calculation of equilibrium properties of mesoscopic systems-for example it is not clear what is the role played by the boundaries and the contacts between the subsystems. We propose here a general definition of the entropy in the equilibrium state, which is applicable to both, macroscopic and mesoscopic systems. This definition still leaves an apparent ambiguity in the definition of the entropy of a mesoscopic system, but this we recognize as the signature of the anthropomorphic character of the entropy (see Jaynes, Am. J. Phys. 33, 391, 1965).To exemplify our approach, we analyze four formulas for the entropy (two for extensive and two for non-extensive entropies) and calculate the equilibrium (canonical) distribution of probabilities by two methods for each. We show that these methods, although widely used, are not equivalent and one of them is a consequence of our definition of the entropy of a compound system. PACS numbers: 05.; 05.90.+m; 02.50.-r

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Foundation of Equilibrium Statistical Mechanics Based on Generalized Entropy

Cited by 4 publications

References 17 publications

Finite size effects in the thermodynamics of a free neutral scalar field

Finite size effects in the thermodynamics of a free neutral scalar field

Ultrarelativistic transverse momentum distribution of the Tsallis statistics

The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies

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