Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics

Shalyt-Margolin, Alexander; Tregubovich, A. Ya.

doi:10.1142/s0217732304012812

Cited by 41 publications

(91 citation statements)

References 21 publications

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“…Besides, QMFL has been framed first using the deformed density matrix and then in the produced corresponding Heisenberg algebra deformation [75][76][77][78][79][80][81][82][83][84], the density matrix deformation ρ(α) in QMFL being a starting object called the density pro-matrix and the deformation parameter (additional parameter) α = l 2 min /x 2 , where x is the measuring scale and l min ∼ l p . As indicated in this paper, the deformation parameter α varies within the limits 0 < α ≤ 1/4.…”

Section: Dark Energy Problem and Quantum Theory With Uv-cutoffmentioning

confidence: 99%

Entropy in the Present and Early Universe: New Small Parameters and Dark Energy Problem

Shalyt-Margolin

2010

Entropy

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It is demonstrated that entropy and its density play a significant role in solving the problem of the vacuum energy density (cosmological constant) of the Universe and hence the dark energy problem. Taking this in mind, two most popular models for dark energy-Holographic Dark Energy Model and Agegraphic Dark Energy Model-are analysed. It is shown that the fundamental quantities in the first of these models may be expressed in terms of a new small dimensionless parameter that is naturally occurring in High Energy Gravitational Thermodynamics and Gravitational Holography (UV-limit). On this basis, the possibility of a new approach to the problem of Quantum Gravity is discussed. Besides, the results obtained on the uncertainty relation of the pair "cosmological constant-volume of space-time", where the cosmological constant is a dynamic quantity, are reconsidered and generalized up to the Generalized Uncertainty Relation.

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Section: Dark Energy Problem and Quantum Theory With Uv-cutoffmentioning

confidence: 99%

Entropy in the Present and Early Universe: New Small Parameters and Dark Energy Problem

Shalyt-Margolin

2010

Entropy

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“…A direct implication of the latter inequality is occurrence of a maximum temperature T max that is inversely proportional to minimal time t min ∼ t p ( [15] expression (11)):…”

Section: Dual Nature Of Parameter τ and Its Temporal Aspectmentioning

confidence: 99%

“…T max [13]- [15]that is associated with the same time point t * min = 2t min . For QMFL this has been noted in the previous section.…”

Section: Dual Nature Of Parameter τ and Its Temporal Aspectmentioning

confidence: 99%

“…When → 0, QM is transformed to the Classical Mechanics. The deformation in Quantum Mechanics at Planck scale takes different paths: commutator deformation or more precisely deformation of the respective Heisenberg algebra [6], [7], [8] and the density matrix deformation approach [9]- [15]. The first approach suffers from two serious disadvantages: 1) the deformation parameter is a dimensional variable κ with a dimension of mass [6]; 2) in the limiting transition to QM this parameter goes to infinity and fluctuations of other values are hardly sensitive to it.…”

Section: Introductionmentioning

confidence: 99%

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The Universe as a Nonuniform Lattice in Finite-Volume Hypercube I: Fundamental Definitions and Particular Features

Shalyt-Margolin

2004

Int. J. Mod. Phys. D

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In this paper a new small parameter associated with the density matrix deformation (density pro-matrix)studied in previous works of the author is introduced into the Generalized Quantum Mechanics (GQM), i.e. quantum mechanics involving description of the Early Universe. It is noted that this parameter has its counterpart in the generalized statistical mechanics. Both parameters offer a number of merits: they are dimensionless, varying over the interval from 0 to 1/4 and assuming in this interval a discreet series of values. Besides, their definitions contain all the fundamental constants. These parameters are very small for the conventional scales and temperatures, e.g. the value of the first parameter is on the order of ≈ 10 −66+2n , where 10 −n is the measuring scale and the Planck scale ∼ 10 −33 cm is assumed. The second one is also too small for the conventional temperatures, that is those much below the Plancks. It is demonstrated that relative to the first of these parameters the Universe may be considered as a nonuniform lattice in the four-dimensional hypercube with dimensionless finite-length * Fax: (+375) 172 326075; e-mail: a.shalyt@mail.ru;alexm@hep.by 1 (1/4) edges. And the time variable is also described by one of the above-mentioned dimensions due to the second parameter and generalized uncertainty relations in thermodynamics. In this context the lattice is understood as a deformation rather than approximation.

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“…For harmonic oscillators and ideal gases in canonical ensembles with GUP see [15]. The deformed density matrix is studied in [16] and modified uncertainty relations for inverse temperature and internal energy are addressed in [17]. Black body radiation with minimal length effects is considered in [18].…”

Section: Introductionmentioning

confidence: 99%

Some Details of Statistical Mechanics of Many-Body Systems in the Presence of a Measurable Minimal Length

Alizadeh

Nozari

2017

Acta Phys. Pol. A

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Different approaches to quantum gravity proposal such as string theory, doubly special relativity, and also black holes physics, all commonly address the existence of a minimal measurable length of the order of the Planck length. One way to apply the minimal length is changing the Heisenberg algebra in the phase space which is known as the generalized uncertainty principle. It is essential to apply this feature on the statistical mechanics of many body systems in the presence of a measurable minimal length scale in order to see the roles of this natural cutoff on physical phenomena. In this paper, some details of statistical mechanics of many body systems that have not been studied carefully in literature are studied in the presence of minimal length scale. The issues such as isomerization, the Liouville theorem, virial theorem and equipartition theorem are studied in this setup with details and the results are explained thoroughly.

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Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics

Cited by 41 publications

References 21 publications

Entropy in the Present and Early Universe: New Small Parameters and Dark Energy Problem

Entropy in the Present and Early Universe: New Small Parameters and Dark Energy Problem

The Universe as a Nonuniform Lattice in Finite-Volume Hypercube I: Fundamental Definitions and Particular Features

Some Details of Statistical Mechanics of Many-Body Systems in the Presence of a Measurable Minimal Length

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