scholarly journals Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations

Entropy ◽  
2014 ◽  
Vol 16 (3) ◽  
pp. 1426-1461 ◽  
Author(s):  
Ramon Álvarez-Estrada
Keyword(s):  
Moment Methods ◽  
Long Time ◽  
Non Equilibrium

scholarly journals Heterogeneous materials: metastable and non-ergodic internal structures

2019 ◽  
Vol 377 (2143) ◽  
pp. 20180353 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Andrey Yu. Zubarev
Keyword(s):  
Magnetic Fields ◽  
Heterogeneous Media ◽  
Heterogeneous Materials ◽  
Computer Methods ◽  
Atomistic Modelling ◽  
Internal Structures ◽  
Long Time ◽  
Biological Polymers ◽  
Physical Mechanics ◽  
Non Equilibrium

This issue is concerned with structural and phase transitions in heterogeneous and composite materials, the effects of external magnetic fields on these phenomena and the macroscopic properties and behaviour of materials with isotropic and anisotropic internal structures. Using experimental, theoretical and computer methods, these transitions are studied at the atomic and mesoscopic levels. The fundamental specific feature of structural transitions in many heterogeneous media consists of the fact that these transitions are stacked for a long time in non-equilibrium states that appear due to either macroscopic dissipative processes (an alternating magnetic field or hydrodynamic flow, for instance) or system lifetime in a metastable state. It is important to explain and describe these transitional states using the general approach of non-equilibrium physical mechanics. The review and research articles in the issue will cover the whole spectrum of scales (from nano to macro) and materials (from metastable liquids to biological polymers) in order to exhibit recently developed trends in the field of heterogeneous materials. Atomistic modelling, structuring induced by external magnetic fields and hydrodynamic flows, metastable and non-ergodic states, mechanical properties and phenomena in heterogeneous materials—all these are covered. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.

scholarly journals Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Milan Radonjic ◽  
Axel Pelster
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Weak Disorder ◽  
Field Approach ◽  
Bose Einstein Condensate ◽  
Adiabatic Switching ◽  
Long Time ◽  
Disorder Potential ◽  
Bose Einstein ◽  
Non Equilibrium

We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially {equilibrated} Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part{, that actually corresponds to adiabatic switching on the disorder,} and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. {We also present an appropriate generalization to inhomogeneous trapped condensates.} Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

scholarly journals Conservation-dissipation formalism of irreversible thermodynamics

2015 ◽  
Vol 40 (2) ◽  
Author(s):  
Yi Zhu ◽  
Liu Hong ◽  
Zaibao Yang ◽  
Wen-An Yong
Keyword(s):  
Evolution Equations ◽  
Maxwell Fluid ◽  
Irreversible Thermodynamics ◽  
Rigid Bodies ◽  
Heat Fluxes ◽  
Coarse Grained ◽  
Irreversible Processes ◽  
State Variables ◽  
Long Time ◽  
Non Equilibrium

AbstractWe propose a conservation-dissipation formalism (CDF) for coarse-grained descriptions of irreversible processes. This formalism is based on a stability criterion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium states tend to equilibrium in long time. As a systematic methodology, CDF provides a feasible procedure in choosing non-equilibrium state variables and determining their evolution equations. The equations derived in CDF have a unified elegant form. They are globally hyperbolic, allow a convenient definition of weak solutions, and are amenable to existing numerics. More importantly, CDF is a genuinely nonlinear formalism and works for systems far away from equilibrium. With this formalism, we formulate novel thermodynamics theories for heat conduction in rigid bodies and non-isothermal compressible Maxwell fluid flows as two typical examples. In these examples, the non-equilibrium variables are exactly the conjugate variables of the heat fluxes or stress tensors. The new theory generalizes Cattaneo's law or Maxwell's law in a regularized and nonlinear fashion.

scholarly journals Non-Equilibrium Entropy and Irreversibility in Generalized Stochastic Loewner Evolution from an Information-Theoretic Perspective

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1098
Author(s):  
Yusuke Shibasaki ◽  
Minoru Saito
Keyword(s):  
Second Law Of Thermodynamics ◽  
Time Behavior ◽  
Information Theoretic ◽  
Stochastic Loewner Evolution ◽  
Loewner Evolution ◽  
Long Time ◽  
Jarzynski Equality ◽  
Gibbs Entropy ◽  
Entropic Measure ◽  
Non Equilibrium

In this study, we theoretically investigated a generalized stochastic Loewner evolution (SLE) driven by reversible Langevin dynamics in the context of non-equilibrium statistical mechanics. Using the ability of Loewner evolution, which enables encoding of non-equilibrium systems into equilibrium systems, we formulated the encoding mechanism of the SLE by Gibbs entropy-based information-theoretic approaches to discuss its advantages as a means to better describe non-equilibrium systems. After deriving entropy production and flux for the 2D trajectories of the generalized SLE curves, we reformulated the system’s entropic properties in terms of the Kullback–Leibler (KL) divergence. We demonstrate that this operation leads to alternative expressions of the Jarzynski equality and the second law of thermodynamics, which are consistent with the previously suggested theory of information thermodynamics. The irreversibility of the 2D trajectories is similarly discussed by decomposing the entropy into additive and non-additive parts. We numerically verified the non-equilibrium property of our model by simulating the long-time behavior of the entropic measure suggested by our formulation, referred to as the relative Loewner entropy.

On exponential long-time evolution in statistical mechanics

1995 ◽  
Vol 448 (1933) ◽  
pp. 293-319 ◽  
Keyword(s):  
Dynamical System ◽  
Banach Space ◽  
Statistical Mechanics ◽  
Time Correlation ◽  
Smoothness Condition ◽  
Time Correlation Functions ◽  
Time Asymmetry ◽  
Discrete Time Dynamical System ◽  
Long Time ◽  
Non Equilibrium

Penrose & Coveney (1994) recently introduced an invertible discrete-time dynamical system called the pastry-cook’s transformation, for which they constructed a ‘canonical’ non-equilibrium ensemble. In the present paper, we apply the Brussels formalism of non-equilibrium statistical mechanics to this system. The use of the formalism is justified rigorously, and the operators which arise in the theory are calculated exactly. The set of ensembles for which the theory is valid is a Banach space of functions satisfying a certain smoothness condition. This condition ensures that ensembles show a decay towards equilibrium, in agreement with the time asymmetry observed in thermodynamics. We also calculate the decay of time correlation functions using Ruelle’s theory of dynamical resonances. We find that all three methods furnish essentially the same description of the exponential decay to equilibrium in this system.

scholarly journals Homeostasis and systematic ageing as non-equilibrium phase transitions in computational multicellular organizations

2019 ◽  
Vol 6 (7) ◽  
pp. 190012
Author(s):  
Yuting Lou ◽  
Ao Chen ◽  
Erika Yoshida ◽  
Yu Chen
Keyword(s):  
Cell Biology ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Field Analysis ◽  
Turnover Rates ◽  
Cycle Arrest ◽  
Long Time ◽  
Division Cell ◽  
Threat To Life ◽  
Non Equilibrium

Being a fatal threat to life, the breakdown of homeostasis in tissues is believed to involve multiscale factors ranging from the accumulation of genetic damages to the deregulation of metabolic processes. Here, we present a prototypical multicellular homeostasis model in the form of a two-dimensional stochastic cellular automaton with three cellular states, cell division, cell death and cell cycle arrest, of which the state-updating rules are based on fundamental cell biology. Despite the simplicity, this model illustrates how multicellular organizations can develop into diverse homeostatic patterns with distinct morphologies, turnover rates and lifespans without considering genetic, metabolic or other exogenous variations. Through mean-field analysis and Monte–Carlo simulations, those homeostatic states are found to be classified into extinctive, proliferative and degenerative phases, whereas healthy multicellular organizations evolve from proliferative to degenerative phases over a long time, undergoing a systematic ageing akin to a transition into an absorbing state in non-equilibrium physical systems. It is suggested that the collapse of homeostasis at the multicellular level may originate from the fundamental nature of cell biology regarding the physics of some non-equilibrium processes instead of subcellular details.

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