Description of instabilities in Uhlenbeck–Ornstein process

Ruscitti, Claudia; Langoni, Laura; Melgarejo, Augusto A.

doi:10.1088/1402-4896/ab2931

Cited by 2 publications

(9 citation statements)

References 15 publications

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“…Our main interest was relating the geometric aspects of the process with the steady-state behavior. In our analysis we used the theoretical framework of the statistical manifold M with α-connections for two different coordinates μ, σ ðÞ and θ 1 , θ 2 ðÞ [4,7]. In the first case, there exist two interesting values of α, namely, α ¼À1 and α ¼ 0, for which the process evolves on a geodesic of space μ, σ ðÞ with different values of τ.…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

“…In the statistical manifold M, we can introduce a natural derivative of the vector field B toward the tangent vector A, denoted by ∇ α A B. It is obtained through the covariant coefficients [7]:…”

Section: Elements Of Statistical Manifoldmentioning

confidence: 99%

“…Considering these parameters as the coordinates μ, σ ðÞ of the manifold M and taking into account Eqs. (2) and (4), it can be seen that for α ¼ 0 and α ¼À1, the system evolves on a geodesic curve [7].…”

Section: Fokker-planck Equation and Macroscopic Potentialmentioning

confidence: 99%

“…In the coordinates μ, σ ðÞ , Eqs. (27) and (29) correspond to the choices α ¼À1 and α ¼ 0, respectively [7]. On the other hand in the context of geometric construction from the potential (Eq.…”

Section: Fokker-planck Equation and Macroscopic Potentialmentioning

confidence: 99%

“…From this probability density function, we build a twodimensional metric-affine manifold in the coordinates μ, σ ðÞ , where μ is the mean and σ the standard deviation. In this coordinates and for the connections α ¼ 0 and α ¼À1, the system evolves on a geodesic curve [7].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Ruscitti¹,

Langoni²,

Melgarejo³

2020

Advances on Tensor Analysis and Their Applications

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The method of Riemannian geometry is fruitful in equilibrium thermodynamics. From the theory of fluctuations it has been possible to construct a metric for the space of thermodynamic equilibrium states. Inspired by these geometric elements, we will discuss the geometric-differential approach of nonequilibrium systems. In particular we will study the geometric aspects from the knowledge of the macroscopic potential associated with the Uhlenbeck-Ornstein (UO) nonequilibrium process. Assuming the geodesic curve as an optimal path and using the affine connection, known as α-connection, we will study the conditions under which a diffusive process can be considered optimal. We will also analyze the impact of this behavior on the entropy of the system, relating these results with studies of instabilities in diffusive processes.

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Section: Discussion and Perspectivesmentioning

confidence: 99%

Section: Elements Of Statistical Manifoldmentioning

confidence: 99%

Section: Fokker-planck Equation and Macroscopic Potentialmentioning

confidence: 99%

Section: Fokker-planck Equation and Macroscopic Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Ruscitti¹,

Langoni²,

Melgarejo³

2020

Advances on Tensor Analysis and Their Applications

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Curvature tensor and collective behavior in a population of bacteria

Oleaga

Ruscitti²,

Langoni³

et al. 2022

Phys. Scr.

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In this work, from a geometric point of view, we analyze the SET model (Schweitzer, Ebeling and Tilch) of the mobility of a bacterium. Biological systems are out of thermodynamic equilibrium and they are subject to complex external or internal influences that can be modeled in the form of noise or fluctuations. In this sense, due to the stochasticity of the variables, we study the probability of finding a bacteria with a speed v in the interval (v; v +dv) or, from a population point of view, we can interpret the probability density function as associated with finding a bacterium with a speed v in the interval (v; v +dv). We carry out this study from the stationary probability density solution of the Fokker-Planck equation and using the structure of the statistical manifold related with the stationary probability density, we study the curvature tensor in terms of two coordinates associated with the state of mobility of the bacteria and the environmental conditions. Taking as reference the geometric interpretations found in the framework of equilibrium thermodynamics, our results suggest that bacteria have an effective repulsive interaction that increases with mobility. These results are compatible with the behavior of populations of bacteria that form biofilms when their mobility decreases.

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Description of instabilities in Uhlenbeck–Ornstein process

Cited by 2 publications

References 15 publications

Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Curvature tensor and collective behavior in a population of bacteria

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