scholarly journals Study of Nonequilibrium Size and Concentration Effects on the Heat and Mass Diffusion of Indistinguishable Particles Using Steepest-Entropy-Ascent Quantum Thermodynamics

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Guanchen Li ◽  
Michael R. von Spakovsky
Keyword(s):  
Spatial Scales ◽  
Local Equilibrium ◽  
Phenomenological Approach ◽  
Mass Diffusion ◽  
Nonequilibrium Process ◽  
First Principle ◽  
Quantum Thermodynamics ◽  
Concentration Effects ◽  
Nonequilibrium Processes ◽  
Far From Equilibrium

Conventional first-principle approaches for studying nonequilibrium processes depend on the mechanics of individual particles or quantum states and as a result require many details of the mechanical features of the system to arrive at a macroscopic property. In contrast, thermodynamics, which has been successful in the stable equilibrium realm, provides an approach for determining macroscopic properties without the mechanical details. Nonetheless, this phenomenological approach is not generally applicable to a nonequilibrium process except in the near-equilibrium realm and under the local equilibrium and continuum assumptions, both of which limit its ability to describe nonequilibrium phenomena. Furthermore, predicting the thermodynamic features of a nonequilibrium process (of entropy generation) across all scales is difficult. To address these drawbacks, steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used. It provides a first-principle thermodynamic-ensemble based approach applicable to the entire nonequilibrium realm even that far-from-equilibrium and does so with a single kinematics and dynamics, which crosses all temporal and spatial scales. Based on prior developments by the authors, SEAQT is used here to study the heat and mass diffusion of indistinguishable particles. The study focuses on the thermodynamic features of far-from-equilibrium state evolution, which is separated from the specific mechanics of individual particle interactions. Results for nonequilibrium size (volume) and concentration effects on the evolutionary state trajectory are presented for the case of high temperature and low particle concentration, which, however, do not impact the generality of the theory and will in future studies be relaxed.

Application of Steepest-Entropy-Ascent Quantum Thermodynamics to Predicting Heat and Mass Diffusion From the Atomistic Up to the Macroscopic Level

2015 ◽  
Author(s):  
Guanchen Li ◽  
Michael R. von Spakovsky
Keyword(s):  
Spatial Scales ◽  
Local Equilibrium ◽  
Phenomenological Approach ◽  
Heat Diffusion ◽  
Quantum Thermodynamics ◽  
Macroscopic Property ◽  
State Evolution ◽  
Equilibrium Process ◽  
Far From Equilibrium ◽  
Non Equilibrium

Conventional first principle approaches for studying non-equilibrium or far-from-equilibrium processes all depend on the mechanics of individual particles or quantum states and as a result, require too many details of the mechanical features of the system to easily or even practically arrive at the value of a macroscopic property. In contrast, thermodynamics, which has been extremely successful in the stable equilibrium realm, provides an approach for determining a macroscopic property without going into the mechanical details. Nonetheless, such a phenomenological approach is not generally applicable to a non-equilibrium process except in the near-equilibrium realm and under the limiting local equilibrium and continuum assumptions, both of which prevent its application across all scales. To address these drawbacks, steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used. It provides an ensemble-based, thermodynamics, first principles approach applicable to the entire non-equilibrium realm even that far-from-equilibrium and does so with a single kinematics and dynamics able to cross all temporal and spatial scales. Based on prior developments by the authors, this paper applies SEAQT to the study of mass and heat diffusion. Specifically, the study focuses on the thermodynamic features of far-from-equilibrium state evolution. Two kinds of size effects on the evolution trajectory, i.e., concentration and volume effects, are discussed.

scholarly journals Nonlinear gyrokinetic Coulomb collision operator

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
R. Jorge ◽  
B. J. Frei ◽  
P. Ricci
Keyword(s):  
Spatial Scales ◽  
Collision Operator ◽  
Multipole Expansion ◽  
Distribution Functions ◽  
Larmor Radius ◽  
Coulomb Collision ◽  
Plasma Dynamics ◽  
Confinement Fusion ◽  
Far From Equilibrium ◽  
Coulomb Collision Operator

A gyrokinetic Coulomb collision operator is derived, which is particularly useful to describe the plasma dynamics at the periphery region of magnetic confinement fusion devices. The derived operator is able to describe collisions occurring in distribution functions arbitrarily far from equilibrium with variations on spatial scales at and below the particle Larmor radius. A multipole expansion of the Rosenbluth potentials is used in order to derive the dependence of the full Coulomb collision operator on the particle gyroangle. The full Coulomb collision operator is then expressed in gyrocentre phase-space coordinates, and a closed formula for its gyroaverage in terms of the moments of the gyrocentre distribution function in a form ready to be numerically implemented is provided. Furthermore, the collision operator is projected onto a Hermite–Laguerre velocity space polynomial basis and expansions in the small electron-to-ion mass ratio are provided.

Phenomenological Approach to Heat Conduction in a One-Dimensional Hard-Point Gas beyond Local Equilibrium

2008 ◽  
Vol 77 (1) ◽  
pp. 014004 ◽  
Author(s):  
Shigeru Taniguchi ◽  
Masashi Nakamura ◽  
Masaru Sugiyama ◽  
Masaharu Isobe ◽  
Nanrong Zhao
Keyword(s):  
Heat Conduction ◽  
Local Equilibrium ◽  
Phenomenological Approach ◽  
One Dimensional

Study of the Transient Behavior and Microstructure Degradation of a SOFC Cathode Using an Oxygen Reduction Model Based on Steepest-Entropy-Ascent Quantum Thermodynamics

2015 ◽  
Author(s):  
Guanchen Li ◽  
Michael R. von Spakovsky
Keyword(s):  
Fuel Cell ◽  
Oxygen Reduction ◽  
Spatial Scales ◽  
Transient Behavior ◽  
Heat Diffusion ◽  
Quantum Thermodynamics ◽  
Sofc Cathode ◽  
State Behavior ◽  
Fuel Cell Cathode ◽  
Non Equilibrium

Oxygen reduction in a solid oxide fuel cell (SOFC) cathode involves a non-equilibrium process of coupled mass and heat diffusion and electrochemical and chemical reactions. These phenomena occur at multiple temporal and spatial scales, from the mesoscopic to the atomistic level, making the modeling, especially in the transient regime, very difficult. Nonetheless, multi-scale models are needed to improve an understanding of oxygen reduction and guide fuel cell cathode design. Existing methods are typically phenomenological or empirical in nature so their application is limited to the continuum realm and quantum effects are not captured. Steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used to model non-equilibrium processes (even those far-from equilibrium) from the atomistic to the macroscopic level. The non-equilibrium relaxation is characterized by the entropy generation, and the study of coupled heat and mass diffusion as well as electrochemical and chemical activity are unified into a single framework. This framework is used here to study the transient and steady state behavior of oxygen reduction in an SOFC cathode system. The result reveals the effects on performance of the different timescales of the varied phenomena involved and their coupling. In addition, the influence of cathode microstructure changes on performance is captured.

Nonlinear Hydrodynamics of Lattice-Gas Automata with Semi-Detailed Balance

1997 ◽  
Vol 08 (04) ◽  
pp. 653-674
Author(s):  
Alberto Suárez ◽  
Jean Pierre Boon
Keyword(s):  
Lattice Boltzmann ◽  
Lattice Gas ◽  
Equilibrium Distribution ◽  
Local Equilibrium ◽  
Transport Coefficients ◽  
Detailed Balance ◽  
Hydrodynamic Equations ◽  
Nonlinear Hydrodynamics ◽  
Far From Equilibrium ◽  
Dynamical Description

Equations governing the evolution of the hydrodynamic variables in a lattice-gas automaton, arbitrarily far from equilibrium, are derived from the micro-dynamical description of the automaton, under the condition that the local collision rules satisfy semi-detailed balance. This condition guarantees that a factorized local equilibrium distribution (for each node) of the Fermi–Dirac form is invariant under the collision step but not under propagation. The main result is the set of fully nonlinear hydrodynamic equations for the automaton in the lattice-Boltzmann approximation; these equations have a validity domain extending beyond the region close to equilibrium. Linearization of the hydrodynamic equations derived here leads to Green–Kubo formulae for the transport coefficients.

scholarly journals Nonequilibrium Process in the σ Model and Chemical Relaxation Time in a Homogeneous Pionic Gas

1997 ◽  
Vol 50 (1) ◽  
pp. 3
Author(s):  
Mitsuru Ishii
Keyword(s):  
Relaxation Time ◽  
Initial Conditions ◽  
Early Stage ◽  
Local Equilibrium ◽  
Heavy Ion ◽  
Nonequilibrium Process ◽  
Ion Collisions ◽  
System A ◽  
Chemical Relaxation ◽  
S Model

In a homogeneous pionic gas system, a chemical nonequilibrium process is understood to have an effect in the expansion processes that are realized immediately after heavy ion collisions. The chemical relaxation time is calculated by incorporating the π+π↔π +π +π+π reaction, which is given in the second order of perturbation in the s model. The π+π↔π +π +π+π reaction is assumed to be less frequent than the π+π↔π +π scattering that is expected to establish the local equilibrium, and the hydrodynamical equation is solved for various initial conditions. It is shown that the relaxation time is of the order of 100 fm and does not have a significant effect on the expansion process, which implies that the pion number freezeout takes place at an early stage of the expansion.

scholarly journals Using a system’s equilibrium behavior to reduce its energy dissipation in nonequilibrium processes

2019 ◽  
Vol 116 (13) ◽  
pp. 5920-5924 ◽  
Author(s):  
Sara Tafoya ◽  
Steven J. Large ◽  
Shixin Liu ◽  
Carlos Bustamante ◽  
David A. Sivak
Keyword(s):  
Friction Coefficient ◽  
Energy Dissipation ◽  
Molecular Machines ◽  
External Control ◽  
Energetic Efficiency ◽  
Square Root ◽  
Nonequilibrium Processes ◽  
Dna Hairpins ◽  
Equilibrium Behavior ◽  
Far From Equilibrium

Cells must operate far from equilibrium, utilizing and dissipating energy continuously to maintain their organization and to avoid stasis and death. However, they must also avoid unnecessary waste of energy. Recent studies have revealed that molecular machines are extremely efficient thermodynamically compared with their macroscopic counterparts. However, the principles governing the efficient out-of-equilibrium operation of molecular machines remain a mystery. A theoretical framework has been recently formulated in which a generalized friction coefficient quantifies the energetic efficiency in nonequilibrium processes. Moreover, it posits that, to minimize energy dissipation, external control should drive the system along the reaction coordinate with a speed inversely proportional to the square root of that friction coefficient. Here, we demonstrate the utility of this theory for designing and understanding energetically efficient nonequilibrium processes through the unfolding and folding of single DNA hairpins.

scholarly journals Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

2016 ◽  
Vol 7 (2) ◽  
pp. 196-222 ◽  
Author(s):  
David Jou ◽  
Vito Antonio Cimmelli
Keyword(s):  
Heat Conduction ◽  
Heat Transport ◽  
Constitutive Equations ◽  
Irreversible Thermodynamics ◽  
Nonequilibrium Processes ◽  
Extended Irreversible Thermodynamics ◽  
Equilibrium Processes ◽  
Far From Equilibrium ◽  
Conceptual Discussion

AbstractWe provide an overview on the problem of modeling heat transport at nanoscale and in far-from-equilibrium processes. A survey of recent results is summarized, and a conceptual discussion of them in the framework of Extended Irreversible Thermodynamics is developed.

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