Time evolution of entropy in a growth model: Dependence on the description

Goh, Segun; Choi, Jae Shi; Choi, Myoungsub; Yoon, B.-G.

doi:10.3938/jkps.70.12

Cited by 6 publications

(8 citation statements)

References 25 publications

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“…In such a case, S env may not behave like a usual thermal particle reservoir, and a more detailed description of the environment, besides the chemical potential, should be provided. In a similar context, albeit in terms of coarse-graining rather than indistinguishability of particles, it has already been reported that the entropy may not be an extensive variable of the system [45]. On the other hand, we can specify the transition rate w s from the equilibrium probability distribution.…”

Section: Connection To the Equilibrium Grand Canonical Descriptionmentioning

confidence: 93%

Grand canonical description of equilibrium and non-equilibrium systems using spin formalism

Goh

Woo

Fortin

et al. 2020

Physica A: Statistical Mechanics and its Applications

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We consider an open system in contact with a reservoir, where particles as well as energies can be exchanged between them, and present a description of the dynamics in terms of mixed (pseudo)spin and state variables. Specifically, a master equation is constructed out of the exchange rates for particles and for energies, which allows us to probe the system in the grand canonical description. In particular, employing the state resummation analysis, we obtain coupled time evolution equations for the probability distributions of the system as well as the environment. This is exemplified by a standard growth model, where the steady-state density function exhibits power-law behavior with the exponent depending on the microscopic parameters of the rate equations.

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Section: Connection To the Equilibrium Grand Canonical Descriptionmentioning

confidence: 93%

Grand canonical description of equilibrium and non-equilibrium systems using spin formalism

Goh

Woo

Fortin

et al. 2020

Physica A: Statistical Mechanics and its Applications

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“…These analyses reveal that the patterns observed in the population distribution involve not only the dispersion across the space but also the asymmetrical change in the shape of the distribution, which we now illuminate with a modeling approach. Log-normal and Weibull distributions emerge naturally from the multiplicative processes with growth and production, which can be described conveniently by master equations [21,22,[37][38][39]. This approach provides lucid elucidation of how the observed distribution emerges as the population grows according to the land-use planning.…”

Section: Growth Of Distribution Functionsmentioning

confidence: 99%

Spatiotemporal distributions of population in Seoul: joint influence of ridership and accessibility of the subway system

et al. 2021

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Moving along with daily life, urban residents and commuters create characteristic spatiotemporal patterns which vary extensively with the time of day. These patterns are formed via traffic flows: accordingly, understanding the impact of transportation system is essential for urban planners to evaluate expected urban activities. To explore them, we examine specifically population distributions in Seoul City by analyzing hourly population data based on mobile phone location records in combination with a couple of indicators of the Seoul Subway system. Through clustering and principal component analyses, we first demonstrate that the spatial distribution of the population is categorized according to the time of day, i.e., night, daytime, and evening, variations across which reflect the morphology of land use. We then examine the influence of the subway system on the population, employing ridership and accessibility as indicators. Our linear regression analysis shows that both are associated with the daytime and the evening populations, which implies that only commercial activities are substantially coupled to the subway system. Further, we find that the distinctive difference of night population is encoded in the probability distributions; this is elucidated by means of a multiplicative growth model for the morphological evolution of Seoul, revealing decentralization of residential areas and centralization of commercial areas. This study sheds light on the interplay of a public transportation system and land use, which is of relevance to planners and policymakers wishing to develop neighborhoods in support of sustainable modes.

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“…It may be interpreted as a quantification of information loss [ 1 , 2 , 3 , 7 , 8 , 9 ]. On the other hand, entropy-based tools have been also proposed to evaluate the propagation of epidemics and related public control interventions (see, for instance, [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ] and some of the references therein). There are also models whose basic framework relies on the use of entropy tools, as for instance [ 13 , 14 , 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

On the Use of Entropy Issues to Evaluate and Control the Transients in Some Epidemic Models

Sen

Nistal

Ibeas

et al. 2020

Entropy

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This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the inter-subpopulations dynamics couplings and the control interventions information through the mentioned time-varying coefficient which drives the basic differential equation model. It is considered a relevant tool the control intervention of the infection along its transient to fight more efficiently against a potential initial exploding transmission. The study is based on the fact that the disease-free and endemic equilibrium points and their stability properties depend on the concrete parameterization while they admit a certain design monitoring by the choice of the control and treatment gains and the use of feedback information in the corresponding control interventions. Therefore, special attention is paid to the evolution transients of the infection curve, rather than to the equilibrium points, in terms of the time instants of its first relative maximum towards its previous inflection time instant. Such relevant time instants are evaluated via the calculation of an “ad hoc” Shannon’s entropy. Analytical and numerical examples are included in the study in order to evaluate the study and its conclusions.

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Time evolution of entropy in a growth model: Dependence on the description

Cited by 6 publications

References 25 publications

Grand canonical description of equilibrium and non-equilibrium systems using spin formalism

Grand canonical description of equilibrium and non-equilibrium systems using spin formalism

Spatiotemporal distributions of population in Seoul: joint influence of ridership and accessibility of the subway system

On the Use of Entropy Issues to Evaluate and Control the Transients in Some Epidemic Models

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