Related Experiment Video
Updated: Aug 9, 2025
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
8.6K
Anomalous finite-size scaling in higher-order processes with absorbing states
Alessandro Vezzani1, Miguel A Muñoz2, Raffaella Burioni3
1Istituto dei Materiali per l'Elettronica ed il Magnetismo (IMEM-CNR), Parco Area delle Scienze, 37/A-43124 Parma, Italy; Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy; and INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy.
Physical Review. E
|February 17, 2023
Summary
This study analyzes birth-death processes on networks using large-deviation theory. We found complex contagion models exhibit wild variability and require advanced methods to capture their behavior.
Area of Science:
- Statistical Physics
- Network Science
- Epidemiology
Background:
- Birth-death processes are fundamental models for population dynamics and spread phenomena.
- Large-deviation theory provides a framework for analyzing rare events and fluctuations in complex systems.
- Higher-order epidemic models, like the q-susceptible-infected-susceptible (q-SIS) model, capture more complex contagion mechanisms.
Purpose of the Study:
- To derive general expressions for the stationary probability distribution of active sites in birth-death processes on networks.
- To analyze the fluctuations and finite-size-scaling properties of these distributions, particularly for the q-SIS model.
- To investigate the necessity of next-to-leading order terms in large-deviation analysis for systems with absorbing states.
Main Methods:
- Application of large-deviation theory (Wentzel-Kramers-Brillouin method) to fully connected birth-death processes.
- Derivation of leading and next-to-leading order terms for the stationary probability distribution.
- Calculation of all moments for the stationary distribution of the q-SIS model.
Main Results:
- A general expression for the stationary probability distribution's leading and next-to-leading terms was obtained.
- The study reproduces existing literature results and derives all moments for the q-SIS model.
- A rich fluctuation scenario was uncovered, with the variance-to-mean ratio diverging at criticality for 1≤q≤3, peaking at q=2, indicating complex contagion behavior.
Conclusions:
- Next-to-leading order terms in large-deviation theory are crucial for accurately describing systems with absorbing states.
- Complex contagion processes exhibit unique scaling properties and significant variability, particularly at criticality.
- The findings highlight the importance of advanced theoretical tools for understanding intricate dynamics in network models.
Related Concept Videos
01:10Entropy Change in Reversible Processes
2.7K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.7K
01:14Reversible and Irreversible Processes
4.4K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
4.4K
01:19Cyclic Processes And Isolated Systems
2.8K
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
2.8K
02:39Entropy
30.5K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
30.5K
01:16Conservation of Mass in Finite Cotrol Volume
1.4K
The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
1.4K
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
103
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
103