Suppression Criterion of the Phase Growth Based on Extremal Principles of Nonequilibrium Thermodynamics

2008 ◽  
Vol 277 ◽  
pp. 39-46
Author(s):  
Yu.A. Lyashenko
Keyword(s):  
Entropy Production ◽  
Critical Thickness ◽  
Nonequilibrium Thermodynamics ◽  
Model System ◽  
Maximal Rate ◽  
Phase Growth ◽  
Binary Phase ◽  
Thermodynamic Criterion ◽  
Extremal Principles ◽  
Kinetic Criterion

The suppression criterion of the binary phase growth due to addition of a third component is considered. In this case the analysis of the two possible criteria of the first phase growth are considered: first – kinetic criterion based on the balance of components fluxes and second - thermodynamic criterion which is based on the maximal rate of the entropy production principle. We demonstrate that in the case of a model system the thermodynamic criterion lead to a bigger value of the critical thickness of the phases which are suppressed by the growth of the investigated phase.

The Sequence of the Phase Growth during Diffusion in Ti-Based Systems

2019 ◽  
Vol 38 (2019) ◽  
pp. 151-157 ◽  
Author(s):  
Bartek Wierzba ◽  
Wojciech J. Nowak ◽  
Daria Serafin
Keyword(s):  
Theoretical Analysis ◽  
Entropy Production ◽  
Diffusion Coefficients ◽  
Intermetallic Phase ◽  
Intermetallic Phases ◽  
Diffusion Couples ◽  
Intrinsic Diffusion ◽  
Phase Growth ◽  
Diffusion Paths

AbstractThe interdiffusion in Ti-based alloys was studied. It was shown that during diffusion at 1,123 K formation of four intermetallic phases occurs. The diffusion paths for six different diffusion couples were determined. Moreover, the entropy production was calculated – the approximation used for determination of the sequence of intermetallic phase formation. In theoretical analysis, the intrinsic diffusion coefficients were determined from the modified Wagner method.

scholarly journals A Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer

Entropy ◽  
2018 ◽  
Vol 20 (3) ◽  
pp. 163 ◽  
Author(s):  
François Gay-Balmaz ◽  
Hiroaki Yoshimura
Keyword(s):  
Heat Transfer ◽  
Entropy Production ◽  
Variational Formulation ◽  
Evolution Equations ◽  
Nonequilibrium Thermodynamics ◽  
Open Systems ◽  
Internal Heat ◽  
Nonholonomic Constraints ◽  
Time Dependent ◽  
Nonlinear Constraint

We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems.

scholarly journals Nonequilibrium Thermodynamics Based on the Distributions Containing Lifetime as a Thermodynamic Parameter

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Vasiliy Vasiliy Ryazanov
Keyword(s):  
Stochastic Processes ◽  
Entropy Production ◽  
Thermodynamic Parameter ◽  
Nonequilibrium Thermodynamics ◽  
Irreversible Thermodynamics ◽  
Statistical Distributions ◽  
Extended Irreversible Thermodynamics ◽  
Nonequilibrium Entropy ◽  
Nonequilibrium States ◽  
Explicit Expressions

To describe the nonequilibrium states of a system, we introduce a new thermodynamic parameter—the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a system by specifying the stochastic processes are written down. The change in the lifetime values by interaction with environment is expressed in terms of fluxes and sources. The expressions for the nonequilibrium entropy, temperature, and entropy production are obtained, which at small values of fluxes coincide with those derived within the frame of extended irreversible thermodynamics. The explicit expressions for the lifetime of a system and its thermodynamic conjugate are obtained.

Dirac structures and variational formulation of port-Dirac systems in nonequilibrium thermodynamics

2020 ◽  
Vol 37 (4) ◽  
pp. 1298-1347
Author(s):  
François Gay-Balmaz ◽  
Hiroaki Yoshimura
Keyword(s):  
Entropy Production ◽  
Variational Formulation ◽  
Nonequilibrium Thermodynamics ◽  
Open Systems ◽  
Ideal Gas ◽  
Irreversible Processes ◽  
Lagrangian Systems ◽  
Specific Class ◽  
Dirac Structures ◽  
Dirac Systems

Abstract The notion of implicit port-Lagrangian systems for nonholonomic mechanics was proposed in Yoshimura & Marsden (2006a, J. Geom. Phys., 57, 133–156; 2006b, J. Geom. Phys., 57, 209–250; 2006c, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto) as a Lagrangian analogue of implicit port-Hamiltonian systems. Such port-systems have an interconnection structure with ports through which power is exchanged with the exterior and which can be modeled by Dirac structures. In this paper, we present the notions of implicit port-Lagrangian systems and port-Dirac dynamical systems in nonequilibrium thermodynamics by generalizing the Dirac formulation to the case allowing irreversible processes, both for closed and open systems. Port-Dirac systems in nonequilibrium thermodynamics can be also deduced from a variational formulation of nonequilibrium thermodynamics for closed and open systems introduced in Gay-Balmaz & Yoshimura (2017a, J. Geom. Phys., 111, 169–193; 2018a, Entropy, 163, 1–26). This is a type of Lagrange–d’Alembert principle for the specific class of nonholonomic systems with nonlinear constraints of thermodynamic type, which are associated to the entropy production equation of the system. We illustrate our theory with some examples such as a cylinder-piston with ideal gas, an electric circuit with entropy production due to a resistor and an open piston with heat and matter exchange with the exterior.

scholarly journals Clausius' entropy revisited

2014 ◽  
Vol 28 (09) ◽  
pp. 1450073 ◽  
Author(s):  
E. G. D. Cohen ◽  
R. L. Merlino
Keyword(s):  
Equilibrium State ◽  
Entropy Production ◽  
Nonequilibrium Thermodynamics ◽  
Local Equilibrium ◽  
Irreversible Processes ◽  
Local Equilibrium State

Conventional nonequilibrium thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper, fluids will be considered in a state of local equilibrium. We argue that the main feature of such systems is not the entropy production, but the organization of the flowing currents in such systems. These currents do not only have entropy production, but must also have an organization needed to flow in a certain direction. It is the latter, which is the source of the equilibrium entropy, when the fluid goes from a local equilibrium state to an equilibrium state. This implies a transmutation of the local equilibrium currents' organization into the equilibrium entropy. Alternatively, when a fluid goes from an equilibrium state to a local equilibrium state, its entropy transmutes into the organization of the currents of that state.

scholarly journals Nonequilibrium Thermodynamics and Distributions Time to Achieve a Given Level of a Stochastic Process for Energy of System

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
V. V. Ryazanov
Keyword(s):  
Stochastic Process ◽  
Entropy Production ◽  
Exponential Distribution ◽  
Nonequilibrium Thermodynamics ◽  
Relaxation Times ◽  
Irreversible Thermodynamics ◽  
Statistical Distribution ◽  
Extended Irreversible Thermodynamics ◽  
Thermodynamic Relationships ◽  
Nonequilibrium Entropy

In a previous paper (Ryazanov (2011)) with the joint statistical distribution for the energy and lifetime (time to achieve a given level of a stochastic process for energy of system) to derive thermodynamic relationships, clarifying similar expressions of extended irreversible thermodynamics we used an exponential distribution of lifetime. In this paper, we explore a more realistic expression for the distribution of time to achieve a given level of a stochastic process for energy of system (or relaxation times or lifetimes), and we analyse how such distribution affects the corresponding expressions of nonequilibrium entropy, temperature, and entropy production.

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