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Understanding Non-Equilibrium Thermodynamics - Springer 2008 Episode 10

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Tham khảo tài liệu 'understanding non-equilibrium thermodynamics - springer 2008 episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 10 Hamiltonian Formalisms A Mathematical Structure of Reversible and Irreversible Dynamics In the theories discussed so far the limitations on the form of the constitutive equations arise essentially from the application of the second law of thermodynamics. However no restrictions were placed on the reversible terms of the time evolution equations as they do not contribute to the entropy production. Such terms may be either gyroscopic forces as Coriolis force or convected time derivatives as Maxwell or corotational derivative which are of frequent use in rheology. It is shown here that requirement of a Hamiltonian structure leads to restrictions on the reversible part of the evolution equations. Hamiltonian formulations have always played a central role not only in mechanics but also in thermodynamics. They have been identified at different levels of description from the microscopic one classical mechanics kinetic theory to the macroscopic one theory of elasticity frictionless fluid flows equilibrium thermodynamics . Despite their theoretical appeal and except rare attempts Hamiltonian methods have not been fully exploited in presence of irreversible effects. The reasons that militate in favour of a Hamiltonian description are numerous the first one is conciseness as the whole set of balance equations are expressed in terms of a limited number of potentials generally one single potential is sufficient. From a practical point of view there exist in parallel powerful numerical methods which have been developed for Hamiltonian systems to obtain approximate solutions as the task of scientists is not only to derive equations but also to find solutions. Moreover besides their power of synthesis and their practical interest Hamiltonian descriptions are also helpful for the physical interpretation of the processes indeed the generating potentials may generally be identified with well-defined physical quantities as the mechanical energy the energy of deformation the