A Lagrangian–Hamiltonian unified formalism for a class of dissipative systems

2018 ◽  
Vol 24 (4) ◽  
pp. 1221-1240
Author(s):  
Hamid Said
Keyword(s):  
Entropy Production ◽  
Hamiltonian Formulation ◽  
Hamiltonian Formalism ◽  
Dissipative Systems ◽  
Internal Variables ◽  
Entropy Production Rate ◽  
Variational Treatment ◽  
Rate Form ◽  
Dynamic Brittle Fracture ◽  
Semilinear Problem

Entropy production in classical thermomechanical systems is the result of three sources: transfer of heat; dissipative stresses, such as viscosity; and internal variables. In this paper, a variational treatment for dissipative systems due to internal variables is presented. Specifically, in the context of the theory of internal variables, a novel dissipative Lagrangian–Hamiltonian formalism is developed. Two fundamental thermodynamic functions (the free energy and the entropy production rate) form the basis of this formalism. The Hamiltonian formulation reveals a new structure on the phase space, and is applied to prove large-time solutions for the semilinear problem. Finally, the formalism is applied to the problem of dynamic brittle fracture.

THE THERMODYNAMIC DESCRIPTION OF HETEROGENEOUS DISSIPATIVE SYSTEMS BY VARIATIONAL METHODS: III. AN APPLICATION OF THE PRINCIPLE OF MINIMUM ENTROPY PRODUCTION TO FLUID DYNAMICS

1964 ◽  
Vol 42 (8) ◽  
pp. 1437-1446 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Thermodynamic Description ◽  
Free Fall ◽  
Dissipative Systems ◽  
Entropy Production Rate ◽  
Stable Steady State ◽  
Minimum Entropy ◽  
Minimum Entropy Production ◽  
Steady State Rate

The stable free-fall flight of a maple seed gives an exceptionally graphic demonstration of the principle of minimum entropy production. Since the rate of entropy production is proportional to the steady-state rate of loss of potential energy, it is visually obvious that the stable rotary configuration represents a minimum of the entropy production rate relative to an unstable steady-state bomblike trajectory. Regarding this phenomenon as the prototype of many practical steady-state fluid-dynamical systems involving rotational modes, we formally demonstrate the possibility of mathematically defining the stable steady-state configuration by means of this variational principle.

The mechanics of granitoid systems and maximum entropy production rates

2010 ◽  
Vol 368 (1910) ◽  
pp. 53-93 ◽  
Author(s):  
Bruce E. Hobbs ◽  
Alison Ord
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Melt Inclusions ◽  
Selection Process ◽  
Finite Thickness ◽  
Control Valve ◽  
Entropy Production Rate ◽  
Constitutive Behaviour ◽  
Maximum Entropy Production ◽  
Physical Height

A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10 4 –10 7 years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson–Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient ‘ponds’ of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic–viscous at high temperatures to elastic–plastic–viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate.

scholarly journals Entropy Production Rate for Avascular Tumor Growth

2011 ◽  
Vol 02 (06) ◽  
pp. 615-620 ◽  
Author(s):  
Elena Izquierdo-Kulich ◽  
Esther Alonso-Becerra ◽  
José M Nieto-Villar
Keyword(s):  
Tumor Growth ◽  
Entropy Production ◽  
Production Rate ◽  
Entropy Production Rate ◽  
Avascular Tumor

Entropy production in polarizable bodies with internal variables

2004 ◽  
Vol 29 (3) ◽  
Author(s):  
Mauro Francaviglia ◽  
Liliana Restuccia ◽  
Patrizia Rogolino
Keyword(s):  
Entropy Production ◽  
Internal Variables

scholarly journals Measurement of entropy production rate in compressible turbulence

2006 ◽  
Vol 76 (4) ◽  
pp. 595-601 ◽  
Author(s):  
M. M Bandi ◽  
W. I Goldburg ◽  
J. R Cressman
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Compressible Turbulence ◽  
Entropy Production Rate

scholarly journals Numerical Investigation into the Development Performance of Gas Hydrate by Depressurization Based on Heat Transfer and Entropy Generation Analyses

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1212 ◽  
Author(s):  
Bo Li ◽  
Wen-Na Wei ◽  
Qing-Cui Wan ◽  
Kang Peng ◽  
Ling-Ling Chen
Keyword(s):  
Heat Transfer ◽  
Energy Loss ◽  
Entropy Production ◽  
Entropy Generation ◽  
Gas Hydrate ◽  
Methane Hydrate ◽  
Dynamic Properties ◽  
Entropy Production Rate ◽  
Entropy Flow ◽  
Hydrate Reservoir

The purpose of this study is to analyze the dynamic properties of gas hydrate development from a large hydrate simulator through numerical simulation. A mathematical model of heat transfer and entropy production of methane hydrate dissociation by depressurization has been established, and the change behaviors of various heat flows and entropy generations have been evaluated. Simulation results show that most of the heat supplied from outside is assimilated by methane hydrate. The energy loss caused by the fluid production is insignificant in comparison to the heat assimilation of the hydrate reservoir. The entropy generation of gas hydrate can be considered as the entropy flow from the ambient environment to the hydrate particles, and it is favorable from the perspective of efficient hydrate exploitation. On the contrary, the undesirable entropy generations of water, gas and quartz sand are induced by the irreversible heat conduction and thermal convection under notable temperature gradient in the deposit. Although lower production pressure will lead to larger entropy production of the whole system, the irreversible energy loss is always extremely limited when compared with the amount of thermal energy utilized by methane hydrate. The production pressure should be set as low as possible for the purpose of enhancing exploitation efficiency, as the entropy production rate is not sensitive to the energy recovery rate under depressurization.

scholarly journals Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 881 ◽  
Author(s):  
Karl Hoffmann ◽  
Kathrin Kulmus ◽  
Christopher Essex ◽  
Janett Prehl
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Irreversible Processes ◽  
Entropy Production Rate ◽  
Continuous Space ◽  
One Dimensional ◽  
Fractional Diffusion Equations ◽  
And Diffusion

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

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