The effects of nonlocality on the evolution of higher order fluxes in non-equilibrium thermodynamics

The role of gradient dependent constitutive spaces is investigated on the example of Extended Thermodynamics of rigid heat conductors. Different levels of nonlocality are developed and the different versions of extended thermodynamics are classified. The local form of the entropy density plays a crucial role in the investigations. The entropy inequality is solved under suitable constitutive assumptions. Balance form of evolution equations is obtained in special cases. Closure relations are derived on a phenomenological level.Comment: 16 pages, 1 figur

Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic theory and projector operator techniques. That equation exhibits violation of the fluctuation dissipation-theorem. By implementing the hydrodynamic regime described by the first moments of the non-equilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose, makes it applicable to more complex situations, often encountered in problems of soft condensed matter, in which not only one but more degrees of freedom are coupled to a non-equilibrium bath.Comment: 10 pages, accepted in Phys. Rev.

Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic theory and projector operator techniques. That equation exhibits violation of the fluctuation dissipation-theorem. By implementing the hydrodynamic regime described by the first moments of the non-equilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose, makes it applicable to more complex situations, often encountered in problems of soft condensed matter, in which not only one but more degrees of freedom are coupled to a non-equilibrium bath.Comment: 10 pages, accepted in Phys. Rev.

Steepest-entropy-ascent quantum thermodynamic modeling of heat and mass diffusion in a far-from-equilibrium system based on a single particle ensemble

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces, which result, are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the non-mutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micro-mechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and near-equilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in near-equilibrium realm.Comment: 15 pages, 4 figure