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Non-equilibrium Phase Transitions
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Non-equilibrium Phase Transitions

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Non-equilibrium Phenomena".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 12438

Special Issue Editors

Prof. Dr. Carlos E. Fiore

E-Mail Website
Guest Editor
Instituto de Física, Universidade de São Paulo, C.P. 66318, São Paulo SP 05315-970, Brazil
Interests: statistical physics; nonequilibrium thermodynamics; phase transitions
Prof. Dr. Silvio C. Ferreira

E-Mail Website
Guest Editor
Departamento de Física, Universidade Federal de Viçosa, Viçosa MG 36570-000, Brazil
Interests: complex networks; nonequilibrium statistical physics; surface growth; mathematical oncology

Special Issue Information

Dear Colleagues,

Nonequilibrium phase transitions is a broad research field emerging in many natural phenomena that operate intrinsically out of the equilibrium, in which the detailed balance and the full theoretical toolbox of equilibrium statistical mechanics are usually not applicable. Nevertheless, fundamental concepts such as universality, criticality and discontinuous transitions have been widely extended to the nonequilibrium realm whose interest have been burst with solid experimental evidences and interdisciplinary applications in the last decade. 

Allied to complex system toolboxes, such as complex networks and stochastic interacting systems, nonequilibrium phase transitions have provided leading contributions to understanding  population dynamics, evolutionary games, cell growth processes, information spreading, contagious diseases and epidemic outbreaks, naming processes, opinion formation, chemical reactions, cryptocurrency dynamics,  brain activity, synchronization, active matter and many other interdisciplinary examples which have attracted increasing interest of scientific community and particularly of the complexity science and statistical physics. 

In particular, ongoing and intensive attention has been recently devoted to the application of nonequilibrium tools, such as absorbing-state phase transitions, disordered systems, entropy production and its usage for typifying phase transitions, nonextensive statistical mechanics, and many others, to build models aiming at describing and predicting the spreading of COVID-19 pandemics in a collaborative synergy with standard epidemiological modeling.

We would like to invite you to contribute to a Special Issue in Entropy entitled "Non-Equilibrium Phase Transitions". The title is deliberately broad and we would hope to gather together a broad spectrum of contributions raging from the foundational to applied problems including theoretical, simulational, and experimental approaches.

Prof. Dr. Carlos E. Fiore
Prof. Dr. Silvio C. Ferreira
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Nonequilibrium phase transitions
  • Absorbing-state phase transitions
  • Disordered systems
  • Spreading of COVID-19 pandemics

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Published Papers (5 papers)

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Research

14 pages, 2020 KiB  
Article
Nonequilibrium Thermodynamics of the Majority Vote Model
by Felipe Hawthorne, Pedro E. Harunari, Mário J. de Oliveira and Carlos E. Fiore
Entropy 2023, 25(8), 1230; https://doi.org/10.3390/e25081230 - 18 Aug 2023
Cited by 4 | Viewed by 1547
Abstract
The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. This model, as well as many other stochastic lattice models, are formulated in terms of stochastic rules with no connection [...] Read more.
The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. This model, as well as many other stochastic lattice models, are formulated in terms of stochastic rules with no connection to thermodynamics, precluding the achievement of quantities such as power and heat, as well as their behaviors at phase transition regimes. Here, we circumvent this limitation by introducing the idea of a distinct and well-defined thermal reservoir associated to each local configuration. Thermodynamic properties are derived for a generic majority vote model, irrespective of its neighborhood and lattice topology. The behavior of energy/heat fluxes at phase transitions, whether continuous or discontinuous, in regular and complex topologies, is investigated in detail. Unraveling the contribution of each local configuration explains the nature of the phase diagram and reveals how dissipation arises from the dynamics. Full article
(This article belongs to the Special Issue Non-equilibrium Phase Transitions)
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15 pages, 604 KiB  
Article
Finite-Size Relaxational Dynamics of a Spike Random Matrix Spherical Model
by Pedro H. de Freitas Pimenta and Daniel A. Stariolo
Entropy 2023, 25(6), 957; https://doi.org/10.3390/e25060957 - 20 Jun 2023
Viewed by 1468
Abstract
We present a thorough numerical analysis of the relaxational dynamics of the Sherrington–Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes N. In the thermodynamic limit and at low temperatures, the perturbation is responsible for a phase transition [...] Read more.
We present a thorough numerical analysis of the relaxational dynamics of the Sherrington–Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes N. In the thermodynamic limit and at low temperatures, the perturbation is responsible for a phase transition from a spin glass to a ferromagnetic phase. We show that finite-size effects induce the appearance of a distinctive slow regime in the relaxation dynamics, the extension of which depends on the size of the system and also on the strength of the non-disordered perturbation. The long time dynamics are characterized by the two largest eigenvalues of a spike random matrix which defines the model, and particularly by the statistics concerning the gap between them. We characterize the finite-size statistics of the two largest eigenvalues of the spike random matrices in the different regimes, sub-critical, critical, and super-critical, confirming some known results and anticipating others, even in the less studied critical regime. We also numerically characterize the finite-size statistics of the gap, which we hope may encourage analytical work which is lacking. Finally, we compute the finite-size scaling of the long time relaxation of the energy, showing the existence of power laws with exponents that depend on the strength of the non-disordered perturbation in a way that is governed by the finite-size statistics of the gap. Full article
(This article belongs to the Special Issue Non-equilibrium Phase Transitions)
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12 pages, 398 KiB  
Article
Synchronization Transition of the Second-Order Kuramoto Model on Lattices
by Géza Ódor and Shengfeng Deng
Entropy 2023, 25(1), 164; https://doi.org/10.3390/e25010164 - 13 Jan 2023
Cited by 5 | Viewed by 2540
Abstract
The second-order Kuramoto equation describes the synchronization of coupled oscillators with inertia, which occur, for example, in power grids. On the contrary to the first-order Kuramoto equation, its synchronization transition behavior is significantly less known. In the case of Gaussian self-frequencies, it is [...] Read more.
The second-order Kuramoto equation describes the synchronization of coupled oscillators with inertia, which occur, for example, in power grids. On the contrary to the first-order Kuramoto equation, its synchronization transition behavior is significantly less known. In the case of Gaussian self-frequencies, it is discontinuous, in contrast to the continuous transition for the first-order Kuramoto equation. Herein, we investigate this transition on large 2D and 3D lattices and provide numerical evidence of hybrid phase transitions, whereby the oscillator phases θi exhibit a crossover, while the frequency is spread over a real phase transition in 3D. Thus, a lower critical dimension dlO=2 is expected for the frequencies and dlR=4 for phases such as that in the massless case. We provide numerical estimates for the critical exponents, finding that the frequency spread decays as ∼t−d/2 in the case of an aligned initial state of the phases in agreement with the linear approximation. In 3D, however, in the case of the initially random distribution of θi, we find a faster decay, characterized by ∼t−1.8(1) as the consequence of enhanced nonlinearities which appear by the random phase fluctuations. Full article
(This article belongs to the Special Issue Non-equilibrium Phase Transitions)
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19 pages, 2237 KiB  
Article
Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation
by Hiroshi Frusawa
Entropy 2022, 24(4), 500; https://doi.org/10.3390/e24040500 - 1 Apr 2022
Cited by 6 | Viewed by 2085
Abstract
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found [...] Read more.
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction. Full article
(This article belongs to the Special Issue Non-equilibrium Phase Transitions)
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15 pages, 6592 KiB  
Article
A Novel Dehumidification Strategy to Reduce Liquid Fraction and Condensation Loss in Steam Turbines
by Yan Yang, Haoping Peng and Chuang Wen
Entropy 2021, 23(9), 1225; https://doi.org/10.3390/e23091225 - 18 Sep 2021
Cited by 9 | Viewed by 2864
Abstract
Massive droplets can be generated to form two-phase flow in steam turbines, leading to erosion issues to the blades and reduces the reliability of the components. A condensing two-phase flow model was developed to assess the flow structure and loss considering the nonequilibrium [...] Read more.
Massive droplets can be generated to form two-phase flow in steam turbines, leading to erosion issues to the blades and reduces the reliability of the components. A condensing two-phase flow model was developed to assess the flow structure and loss considering the nonequilibrium condensation phenomenon due to the high expansion behaviour in the transonic flow in linear blade cascades. A novel dehumidification strategy was proposed by introducing turbulent disturbances on the suction side. The results show that the Wilson point of the nonequilibrium condensation process was delayed by increasing the inlet superheated level at the entrance of the blade cascade. With an increase in the inlet superheated level of 25 K, the liquid fraction and condensation loss significantly reduced by 79% and 73%, respectively. The newly designed turbine blades not only remarkably kept the liquid phase region away from the blade walls but also significantly reduced 28.1% averaged liquid fraction and 47.5% condensation loss compared to the original geometry. The results provide an insight to understand the formation and evaporation of the condensed droplets inside steam turbines. Full article
(This article belongs to the Special Issue Non-equilibrium Phase Transitions)
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