A check of Prigogine’s theorem of minimum entropy production in a rod in a nonequilibrium stationary state

Based on the irreversible thermodynamics, a irreversible thermodynamic description of domain occurrences in ferroics such as ferroelectrics, ferromagnetics and ferroelastics was given. The ferroic domain structures occur at the ferroic phase transitions from the prototype phases to the ferroic phases. The processes of transition are stationary state processes so that the principle of minimum entropy production is satisfied. The domain occurrences are a consequence of this principle. The time-spatial symmetry related to the domains and their occurrences was also expounded.

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Thermodynamic Extremum Principles for Nonequilibrium Stationary State in Heat Conduction

Journal of Heat Transfer ◽

10.1115/1.4036086 ◽

2017 ◽

Vol 139 (7) ◽

Author(s):

Yangyu Guo ◽

Ziyan Wang ◽

Moran Wang

Keyword(s):

Thermal Conductivity ◽

Heat Conduction ◽

Stationary State ◽

Transient Heat Conduction ◽

Clear Understanding ◽

Minimum Entropy ◽

Dissipation Potential ◽

Nonequilibrium Stationary State ◽

Minimum Entropy Production ◽

Constant Thermal Conductivity

Minimum entropy production principle (MEPP) is an important variational principle for the evolution of systems to nonequilibrium stationary state. However, its restricted validity in the domain of Onsager's linear theory requires an inverse temperature square-dependent thermal conductivity for heat conduction problems. A previous derivative principle of MEPP still limits to constant thermal conductivity case. Therefore, the present work aims to generalize the MEPP to remove these nonphysical limitations. A new dissipation potential is proposed, the minimum of which thus corresponds to the stationary state with no restriction on thermal conductivity. We give both rigorous theoretical verification of the new extremum principle and systematic numerical demonstration through 1D transient heat conduction with different kinds of temperature dependence of the thermal conductivity. The results show that the new principle remains always valid while MEPP and its derivative principle fail beyond their scopes of validity. The present work promotes a clear understanding of the existing thermodynamic extremum principles and proposes a new one for stationary state in nonlinear heat transport.

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The principle of minimum entropy production and snow structure

Journal of Glaciology ◽

10.3189/172756504781829945 ◽

2004 ◽

Vol 50 (170) ◽

pp. 342-352 ◽

Cited By ~ 3

Author(s):

Perry Bartelt ◽

Othmar Buser

Keyword(s):

Mass Transfer ◽

Temperature Gradient ◽

Entropy Production ◽

Surface Curvature ◽

The State ◽

Temperature Gradients ◽

Curvature Radius ◽

Minimum Entropy ◽

Snow Layer ◽

Minimum Entropy Production

AbstractAn essential problem in snow science is to predict the changing form of ice grains within a snow layer. Present theories are based on the idea that form changes are driven by mass diffusion induced by temperature gradients within the snow cover. This leads to the well-established theory of isothermal- and temperature-gradient metamorphism. Although diffusion theory treats mass transfer, it does not treat the influence of this mass transfer on the form — the curvature radius of the grains and bonds — directly. Empirical relations, based on observations, are additionally required to predict flat or rounded surfaces. In the following, we postulate that metamorphism, the change of ice surface curvature and size, is a process of thermodynamic optimization in which entropy production is minimized. That is, there exists an optimal surface curvature of the ice grains for a given thermodynamic state at which entropy production is stationary. This state is defined by differences in ice and air temperature and vapor pressure across the interfacial boundary layer. The optimal form corresponds to the state of least wasted work, the state of minimum entropy production. We show that temperature gradients produce a thermal non-equilibrium between the ice and air such that, depending on the temperature, flat surfaces are required to mimimize entropy production. When the temperatures of the ice and air are equal, larger curvature radii are found at low temperatures than at high temperatures. Thus, what is known as isothermal metamorphism corresponds to minimum entropy production at equilibrium temperatures, and so-called temperature-gradient metamorphism corresponds to minimum entropy production at none-quilibrium temperatures. The theory is in good agreement with general observations of crystal form development in dry seasonal alpine snow.

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