A sketch of continuum thermodynamics

Abstract Different formulations of non-equilibrium continuum thermodynamics are discussed: Thermodynamics of Irreversible Processes (TIP), Rational Thermodynamics (RAT), Extended Thermodynamics (ET), Mesoscopic Continuum Thermodynamics (MT), and the GENERIC version of thermodynamics. Concepts as constitutive quantity, state space, material frame indifference, exploiting dissipation inequality, mesoscopic variables, and GENERIC balance equations are taken into consideration.

[1]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[2]  Ehrentraut,et al.  Viscosity coefficients of partially aligned nematic and nematic discotic liquid crystals. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  F. M. Leslie Some constitutive equations for liquid crystals , 1968 .

[4]  G. Lebon,et al.  Recent Developments in Nonequilibrium Thermodynamics , 1984 .

[5]  A. Cental Eringen,et al.  Part I – Polar Field Theories , 1976 .

[6]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. I. Development of a general formalism , 1997 .

[7]  I. Muller,et al.  Zum Paradoxon der Warmeleitungstheorie , 1967 .

[8]  I-Shih Liu,et al.  Method of Lagrange multipliers for exploitation of the entropy principle , 1972 .

[9]  W. Muschik A PHENOMENOLOGICAL FOUNDATION OF NON-LINEAR OC-RECIPROCAL RELATIONS (IRREVERSIBLE THERMODYNAMICS APPROACH) , 1998 .

[10]  G. Maugin The Thermomechanics of Plasticity and Fracture , 1992 .

[11]  W. Muschik Fundamentals of Nonequilibrium Thermodynamics , 1993 .

[12]  C. C. Wang,et al.  A new representation theorem for isotropic functions: An answer to Professor G. F. Smith's criticism of my papers on representations for isotropic functions , 1970 .

[13]  K. Hutter,et al.  Continuum Description of the Dynamics and Thermodynamics of Phase Boundaries Between Ice and Water, Part I. Surface Balance Laws and their Interpretation in Terms of Three-Dimensional Balance Laws Averaged over the Phase Change Boundary Layer , 1988 .

[14]  W. Muschik,et al.  A concept of non-equilibrium temperature , 1977 .

[15]  Jean Lemaitre,et al.  A Course on Damage Mechanics , 1992 .

[16]  J. Straley,et al.  Physics of liquid crystals , 1974 .

[17]  W. Muschik A Phenomenological Foundation of Non-linear Onsager-Casimir Reciprocity Relations , 1977 .

[18]  Hans Christian Öttinger,et al.  General projection operator formalism for the dynamics and thermodynamics of complex fluids , 1998 .

[19]  W. Muschik,et al.  Orientational Balances ffor Nematic Liquid Crystals , 1991 .

[20]  On Symmetric irreducible tensors in d-dimensions , 1998 .

[21]  Brian J. Edwards,et al.  Non-canonical Poisson bracket for nonlinear elasticity with extensions to viscoelasticity , 1991 .

[22]  W. Muschik,et al.  Macroscopic constitutive equations for liquid crystals induced by their mesoscopic orientation distribution , 1992 .

[23]  W. Müller,et al.  Bilanzgleichungen offener mehrkomponentiger Systeme. I. Massen- und Impulsbilanzen , 1983 .

[24]  W. Muschik Formulations of the second law—Recent developments , 1988 .

[25]  Frederick Reif,et al.  Statistische Physik und Theorie der Wärme , 1987 .

[26]  Miroslav Grmela,et al.  Bracket formulation of dissipative fluid mechanics equations , 1984 .

[27]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[28]  D. W. Condiff,et al.  Transport Mechanics in Systems of Orientable Particles , 1969 .

[29]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

[30]  W. Muschik Empirical foundation and axiomatic treatment of non-equilibrium temperature , 1977 .

[31]  Gérard A. Maugin,et al.  THERMODYNAMICS WITH INTERNAL VARIABLES , 1999 .

[32]  W. Muschik,et al.  A continuum theory for liquid crystals describing different degrees of orientational order , 1993 .

[33]  Gianfranco Capriz,et al.  Continua with Microstructure , 1989 .

[34]  W. Muschik Objectivity and frame indifference, revisited , 1998 .

[35]  E. Cosserat,et al.  Théorie des Corps déformables , 1909, Nature.

[36]  P. Gennes,et al.  The physics of liquid crystals , 1974 .

[37]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[38]  C. Truesdell,et al.  On the Pressures and the Flux of Energy in a Gas according to Maxwell's Kinetic Theory, II , 1956 .

[39]  Krzysztof Wilmański,et al.  Thermomechanics of Continua , 1998 .

[40]  I-Shih Liu,et al.  Extended thermodynamics of classical and degenerate ideal gases , 1983 .

[41]  Issam Doghri,et al.  Nonlinear continuum mechanics , 2000 .

[42]  G. Lebon,et al.  Extended irreversible thermodynamics , 1993 .

[43]  J. Ericksen,et al.  Poiseuille flow of certain anisotropic fluids , 1961 .

[44]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism , 1997 .

[45]  G. Maugin,et al.  Thermodynamic Modelling of Polymers in Solution , 1988 .

[46]  W. Muschik,et al.  Statistical foundation of macroscopic balances for liquid crystals in alignment tensor formulation , 1991 .

[47]  W. Muschik,et al.  Orientation-Balances for Liquid Crystals and Their Representation by Alignment Tensors , 1991 .

[48]  Bernard D. Coleman,et al.  Existence of Caloric Equations of State in Thermodynamics , 1964 .

[49]  W. Müller,et al.  Bilanzgleichungen offener mehrkomponentiger Systeme. II. Energie- und Entropiebilanz , 1983 .

[50]  D. Jou,et al.  Nonlinear and Hamiltonian extended irreversible thermodynamics , 1998 .

[51]  W. Muschik,et al.  An Amendment to the Second Law , 1996 .

[52]  A. Cemal Eringen,et al.  NONLINEAR THEORY OF SIMPLE MICRO-ELASTIC SOLIDS-I , 1964 .

[53]  C. Papenfuss,et al.  Concepts of Mesoscopic Continuum Physics With Application to Biaxial Liquid Crystals , 2000 .