Lee and Stanley reply:

Lee, Jysoo; Stanley, H. Eugene

doi:10.1103/physrevlett.63.1190

Cited by 22 publications

(38 citation statements)

References 3 publications

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“…Several investigators have studied the equilibrium statistical mechanics of the gas of non-interacting q-bosons [6][7][8][9][10][11][12][13][14]. We shall now briefly discuss some of the important results from these studies before introducing our formulation of the thermostatistics of q-deformed bosons.…”

Section: Thermal Averages and Statistical Distribution For Q-bosmentioning

confidence: 99%

“…In the grand canonical ensemble, the Hamiltonian of the non-interacting boson gas is expected to have the following form [6][7][8][9]…”

Section: Thermal Averages and Statistical Distribution For Q-bosmentioning

confidence: 99%

“…One interesting realization of the first approach is the study of exactly solvable statistical systems which has led to a new algebra, the q-deformed algebra of creation and annihilation operators, usually called q-bosons (q-fermions) or q-oscillators and related to the general theory of quantum groups [4,5]. Many recent investigations in the theory of q-bosons have provided much insight into both the mathematical development and the q-deformed thermodynamics [6][7][8][9][10][11][12][13][14]. However, we believe that a fully consistent formulation connecting the statistical mechanics and the thermodynamics (i.e., thermostatistics) of q-bosons has been lacking.…”

Section: Introductionmentioning

confidence: 99%

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Thermostatistics of aq-deformed boson gas

2000

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We show that a natural realization of the thermostatistics of q bosons can be built on the formalism of q calculus, and that the entire structure of thermodynamics is preserved if we use an appropriate Jackson derivative in place of the ordinary thermodynamics derivative. This framework allows us to obtain a generalized q boson entropy which depends on the q basic number. We study the ideal q boson gas in the thermodynamic limit which is shown to exhibit Bose-Einstein condensation with a higher critical temperature and a discontinuous specific heat.

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Section: Thermal Averages and Statistical Distribution For Q-bosmentioning

confidence: 99%

“…In the grand canonical ensemble, the Hamiltonian of the non-interacting boson gas is expected to have the following form [6][7][8][9]…”

Section: Thermal Averages and Statistical Distribution For Q-bosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermostatistics of aq-deformed boson gas

2000

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“…In DLA this analogous maximum energy is given by the smallest value of all the growth probabilities: amax = -In (P(min))/ln L [7]. Hence, by using (12), we expect P(min) to satisfy where A glance into these equations indicates that for the particular case in which q -L -+ a, we have -In P(min) z (In L)' in accordance with some numerical simulations [8].…”

Section: Connection With Dla Systemsmentioning

confidence: 99%

Multifractal Properties of Diffusion‐Limited Aggregates and Random Multiplicative Processes

Canessa¹

1991

Physica Status Solidi (b)

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The multifractal properties are considered of irreversible diffusion-limited aggregation (DLA) from the point of view of the self-similarity of fluctuations in random multiplicative processes. In particular the breakdown of rnultifractal behaviour and phase transition associated with the negative moments of the growth probabilities in DLA are analysed.Die Multifraktaleigenschaften der irreversiblen diffusionsbegrenzten Aggregation (DLA) werden vom Standpunkt der Selbstahnlichkeit von Fluktuationen in statistischen multiplikativen Prozessen untersucht. lnsbesondere werden das Verschwinden des Multifraktalverhaltens und des mit den negativen Momenten der Wachstumswahrscheinlichkeiten in der DLA verkniipften Phasenubergangs analysiert.

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“…We first give an overview of the origins and fundamental principles of the paradox, in a largely nontechnical perspective suitable for supporting the subsequent discussions. The paradox was first conceptualized as an abstraction of the phenomenon of flashing Brownian ratchets, [2][3][4][5][6][7][8][9] wherein diffusive particles exhibit unexpected drift when exposed to alternating periodic potentials. It has since been applied across a multitude of neighboring disciplines in the physical sciences and engineering-related fields, [10,11] such as diffusive and granular flow dynamics, [12][13][14] information thermodynamics, [15][16][17][18] chaos theory, [19][20][21][22][23][24][25] switching problems, [26][27][28] and quantum phenomena; [29][30][31][32][33][34][35][36][37][38] but a plethora of exciting applications has also been found in biology, which this paper focuses upon.…”

Section: Introductionmentioning

confidence: 99%

Paradoxical Survival: Examining the Parrondo Effect across Biology

2019

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Parrondo's paradox, in which losing strategies can be combined to produce winning outcomes, has received much attention in mathematics and the physical sciences; a plethora of exciting applications has also been found in biology at an astounding pace. In this review paper, the authors examine a large range of recent developments of Parrondo's paradox in biology, across ecology and evolution, genetics, social and behavioral systems, cellular processes, and disease. Intriguing connections between numerous works are identified and analyzed, culminating in an emergent pattern of nested recurrent mechanics that appear to span the entire biological gamut, from the smallest of spatial and temporal scales to the largest—from the subcellular to the complete biosphere. In analyzing the macro perspective, the pivotal role that the paradox plays in the shaping of biological life becomes apparent, and its identity as a potential universal principle underlying biological diversity and persistence is uncovered. Directions for future research are also discussed in light of this new perspective.

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Lee and Stanley reply:

Cited by 22 publications

References 3 publications

Thermostatistics of aq-deformed boson gas

Thermostatistics of aq-deformed boson gas

Multifractal Properties of Diffusion‐Limited Aggregates and Random Multiplicative Processes

Paradoxical Survival: Examining the Parrondo Effect across Biology

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