Continuum Thermodynamics of the GluoN_c Plasma

We study the thermodynamics of SU(N_c) pure gauge theories for N_c=3, 4 and 6. The continuum and thermodynamic limits of bulk quantities such as the pressure, energy density and the entropy density are taken by using several different lattice spacings and volumes. There is no window of temperature in which a non-trivial conformal theory describes bulk thermodynamics. We extract the latent heat of the first-order deconfinement phase transitions and observe good scaling with N_c. For all quantities that we measure, strong N_c scaling holds, except, possibly, very close to the transition temperature, T_c; however we are unable to find strong evidence for scaling with the 't Hooft coupling in thermal quantities at the small values of N_c which we study

Continuum thermodynamics of chemically reacting fluid mixtures

We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate definition of thermal energy excluding diffusive contributions. The resulting interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric in case of binary interactions. For chemically reacting systems and as a new result, the chemical interaction force is a contribution being non-symmetric outside of chemical equilibrium. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations. Moreover, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations become a strict consequence. With a classification of the factors in the binary products of the entropy production according to their parity--instead of the classical partition into so-called fluxes and driving forces--the apparent anti-symmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared to the speed of sound, the Maxwell-Stefan equations follow in the case without chemistry, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model with only mass being balanced individually. In the reactive case ..

Continuum thermodynamics and phase-field models

1Phase transitions between two phases are modelled as space regions where a phase-field changes smoothly. The two phases are separated by a thin transition layer, the so-called diffuse interface. All thermodynamic quantities are allowed to vary inside this layer, including the pressure and the mass density. A thermodynamic approach is developed by allowing for the nonlocal character of the continuum. It is based on an extra entropy flux which is proved to be non vanishing inside the transition layer, only. The phase-field is regarded as an internal variable and the kinetic or evolution equation is viewed as a constitutive equation of rate type. Necessary and sufficient restrictions placed by thermodynamics are derived for the constitutive equations and, furthermore, a general form of the evolution equation for the phase-field is obtained within the schemes of both a non-conserved and a conserved phase-field. Based on the thermodynamic restrictions, a phase-field model for the ice-water transition is established which allows for superheating and undercooling. A model ruling the liquid-vapor phase transition is also provided which accounts for both temperature and pressure variations during the evaporation process. The explicit expression of the Gibbs free enthalpy, the Clausius-Clapeyron formula and the customary form of the vapor pressure curve are recovered.Mathematics Sub ject Classification (2000). Primary 82B26; Secondary 82C26, 80A22openopenC. GIORGIGiorgi, Claudi

Entropy Production and Equilibrium Conditions of General-Covariant Spin Systems

In generalizing the special-relativistic one-component version of Eckart's continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry, we consider the entropy production and other themodynamical quantities such as the entropy flux and the Gibbs fundamental equation. We discuss equilibrium conditions in gravitational theories which are based on such geometries. In particular, thermodynamic implications of the non-symmetry of the energy-momentum tensor and the related spin balance equations are investigated, also for the special case of General Relativity.Comment: General-covariant spin systems are carefully discussed in the framework of non-equlibrium thermodynamics starting out with an already published entropy identit

On a continuum thermodynamics formulation and computational aspects of finite growth in soft tissues

17 pagesInternational audienceIn this paper, we try to settle the bases of a concise modelling of growth within the unified framework of continuum thermodynamics. Special emphasis is placed on the modelling of soft biological tissues at finite strains. For this, we adopt the nowadays well-known kinematic assumption of a multiplicative decomposition of the deformation gradient into an elastic part and a growth part. It is shown how continuum thermodynamics is crucial in setting convenient forms for the coupling between stress and growth in general. The particularization to isotropy simplifies considerably the growth modelling from both the theoretical and the numerical points of view. Simple growth constitutive equations are proposed and embedded into a finite element context. Finally, representative numerical examples examining stress-dependent growth and residual stress arising from growth and resorption close this study

Continuum thermodynamics of chemically reacting fluid mixtures

We consider viscous and heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, a first main aim is the derivation of a closed system of partial mass and partial momentum balances plus a common balance of internal energy. This is achieved by careful exploitation of the entropy principle which, in particular, requires appropriate definitions of absolute temperature and chemical potentials based on an adequate definition of thermal energy that excludes diffusive contributions. The latter is crucial in order to obtain a closure framework for the interaction forces between the different species. The interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric if binary interactions are assumed. In the non-reactive case, this leads to a system of Navier-Stokes type sub-systems, coupled by interspecies friction forces. For chemically reacting systems and as a new result, the chemical interaction force is identified as a contribution which is non-symmetric, unless chemical equilibrium holds. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations which is common in the engineering literature. Moreover, starting with a continuum thermodynamic field theory right away, local versions of fundamental relations known from thermodynamics of homogeneous systems, like the Gibbs-Duhem equation, are derived. Furthermore, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations are a strict consequence. With a classification of the factors forming the binary products in the entropy production according to their parity instead of the classical distinction between so-called fluxes and driving forces, the apparent anti-symmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared to the speed of sound, the well-known Maxwell-Stefan equations together with the so-called generalized thermodynamic driving forces follow in the special case without chemical reactions, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model having only the constituents mass balances individually. In the reactive case, this approximation via a scale separation argument is no longer possible. Instead, we first employ the partial mass and mixture internal energy balances, common to both model classes, to identify all constitutive quantities. Combined with the concept of entropy invariant model reduction, leaving the entropy production unchanged under the reduction from partial momentum balances to a single common mixture momentum balance, the chemical interactions yield an additional contribution to the transport coefficients, leading to an extension of the Maxwell-Stefan equations to chemically active mixtures. Within the considered model class for reactive fluid mixtures the new results are achieved for arbitrary free energy functions

Elastic, thermal expansion, plastic and rheological processes - theory and experiment

Rocks are important examples for solid materials where, in various engineering situations, elastic, thermal expansion, rheological/viscoelastic and plastic phenomena each may play a remarkable role. Nonequilibrium continuum thermodynamics provides a consistent way to describe all these aspects in a unified framework. This we present here in a formulation where the kinematic quantities allow arbitrary nonzero initial (e.g., in situ) stresses and such initial configurations which - as a consequence of thermal or remanent stresses - do not satisfy the kinematic compatibility condition. The various characteristic effects accounted by the obtained theory are illustrated via experimental results where loaded solid samples undergo elastic, thermal expansion and plastic deformation and exhibit rheological behaviour. From the experimental data, the rheological coefficients are determined, and the measured temperature changes are also explained by the theory.Comment: 15 pages, to appear in Period. Polytech. Civil En