The role of nonequilibrium fluxes in the relaxation processes of the linear chemical master equation
Abstract
We propose a nonequilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a nonequilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their “far from equilibrium behavior,” hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the nonequilibrium chemical fluxes. For systems in NESS, we show that there is a nonconservative “external vector field” whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of thesemore »
 Authors:
 Physics and Astronomy Department, Bologna University and INFN Sezione di Bologna (Italy)
 Publication Date:
 OSTI Identifier:
 22420043
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CHAIN REACTIONS; MOLECULES; NUMERICAL ANALYSIS; PLASTICITY; RELAXATION TIME
Citation Formats
Oliveira, Luciana Renata de, Bazzani, Armando, Giampieri, Enrico, and Castellani, Gastone C., Email: Gastone.Castellani@unibo.it. The role of nonequilibrium fluxes in the relaxation processes of the linear chemical master equation. United States: N. p., 2014.
Web. doi:10.1063/1.4891515.
Oliveira, Luciana Renata de, Bazzani, Armando, Giampieri, Enrico, & Castellani, Gastone C., Email: Gastone.Castellani@unibo.it. The role of nonequilibrium fluxes in the relaxation processes of the linear chemical master equation. United States. doi:10.1063/1.4891515.
Oliveira, Luciana Renata de, Bazzani, Armando, Giampieri, Enrico, and Castellani, Gastone C., Email: Gastone.Castellani@unibo.it. Thu .
"The role of nonequilibrium fluxes in the relaxation processes of the linear chemical master equation". United States.
doi:10.1063/1.4891515.
@article{osti_22420043,
title = {The role of nonequilibrium fluxes in the relaxation processes of the linear chemical master equation},
author = {Oliveira, Luciana Renata de and Bazzani, Armando and Giampieri, Enrico and Castellani, Gastone C., Email: Gastone.Castellani@unibo.it},
abstractNote = {We propose a nonequilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a nonequilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their “far from equilibrium behavior,” hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the nonequilibrium chemical fluxes. For systems in NESS, we show that there is a nonconservative “external vector field” whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the nonequilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the nonequilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the “plasticity property” of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.},
doi = {10.1063/1.4891515},
journal = {Journal of Chemical Physics},
number = 6,
volume = 141,
place = {United States},
year = {Thu Aug 14 00:00:00 EDT 2014},
month = {Thu Aug 14 00:00:00 EDT 2014}
}

A nonlogarithmic time dependence of the magnetization relaxation in superconductors is modeled by certain solutions of the nonlinear equation for flux diffusion, which can be derived either on the assumption of a logarithmic dependence of the pinning potential on the current density or, equivalently, a powerlaw currentvoltage characteristic. Limiting cases of the spatiotemporal evolution of the flux density profile are identified: at one end of the parameters governing nonlinearity the classical, linear processes relevant to the reversible part of the HT diagram of high{Tc} materials are found, whereas at the other end, a true criticalstate behavior emerges. Scaling relations betweenmore »

Nonequilibrium effects upon the nonMarkovian CaldeiraLeggett quantum master equation
Highlights: > Classical Brownian motion described by a nonMarkovian FokkerPlanck equation. > Quantization process. > Quantum Brownian motion described by a nonMarkovian CaldeiraLeggett equation. > A nonequilibrium quantum thermal force is predicted.  Abstract: We obtain a nonMarkovian quantum master equation directly from the quantization of a nonMarkovian FokkerPlanck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a nonthermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a nonMarkovian CaldeiraLeggett master equation on the basis of which we work out the conceptmore » 
Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium
The stochastic thermodynamics of a dilute, wellstirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochasticthermodynamic description is only valid at a detailedbalanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » 
Unified EinsteinVirasoro Master Equation in the General NonLinear Sigma Model
The Virasoro master equation (VME) describes the general affineVirasoro constructionmore » 
Chemical kinetics and relaxation of nonequilibrium air plasma generated by energetic photon and electron beams
The comprehension of electromagnetic perturbations of electronic devices, due to air plasmainduced electromagnetic field, requires a thorough study on air plasma. In the aim to understand the phenomena at the origin of the formation of nonequilibrium air plasma, we simulate, using a volume average chemical kinetics model (0D model), the time evolution of a nonequilibrium air plasma generated by an energetic Xray flash. The simulation is undertaken in synthetic air (80% N{sub 2} and 20% O{sub 2}) at ambient temperature and atmospheric pressure. When the Xray flash crosses the gas, nonrelativistic Compton electrons (low energy) and a relativistic Compton electronmore »