Volume 27, Issue 4

Heat engine models, starting from the most fundamental Carnot case, are analyzed. Two major methods of viewing the power plant as a thermodynamic heat engine are presented and studied. Realistic models are sought by introducing internal heat transport or bypass heat leak treatments. Simple treatments are presented to convey the general modeling ideas without unnecessary complications. Some new results are obtained and certain old results are commented on.

A gradient theory with internal variables in a rigid heat conductor is developed. The Second Law of thermodynamics is exploited to argue suitable boundary conditions. Comparison is made with different approaches which have appeared in the recent literature.

We explore the relation of a line of studies over the last dozen years on mesoscale material response below the Representative Volume Element with the line of studies on mesoscopic continuum physics. The objective is the development of stochastic continuum thermodynamics able to grasp random microstructural features absent in deterministic continuum theories. We first compare two lines of studies–those dealing with the response on a scale smaller than the Representative Volume Element (RVE) vis-à-vis those on mesoscopic continuum physics–and observe the dilemma of choice of the random field approximation. As a common basis for connecting both approaches, we propose a mesoscale Statistical Volume Element (SVE) and consider bounding its response via two admissible loadings. Employing the paradigm of thermal conductivity, we also present the relevant Legendre transformations. The latter are then generalized to the more general situation of fields governed by a quartet of Legendre transformations.

A two-phase model is considered which resolves both the thermodynamics of the two phases and of the interface, as well as the morphology in terms of Minkowski functionals, as scalar morphological variables, assuming equal velocities of the phases. In order to discuss whether, in compressible flow, the morphological variables should transform as scalars, as scalar densities or as a mixture of both, the two-phase model is cast into the GENERIC framework of non-equilibrium thermodynamics. The Jacobi identity, representing the time structure invariance of the reversible dynamics, is found not to impose any restrictions on the convection of the morphological variables, i.e., on the divergence terms of the velocity field appearing in their evolution equations. As an application of the general compressible two-phase model, the implications of assuming both equal velocities and equal temperatures of the phases are elaborated. In particular, it is found that in such a description the volume fraction and the amount of interface per unit volume are neither scalars nor scalar densities, their intermediate convection mechanism being completely determined in terms of the material properties of the phases.

Using a phenomenological approach, we analyse the formation and the propagation of the patterns (or ‘dissipative structures’) in the stock market, the spatial coordinate being the bid-offer spread y, as a function of which the spectrum φ of deals is modelled. The stock market will be considered a distributed active medium that is a set of active elements (the brokers) interacting with others through deals (typically a diffusion process). The physical model used is the reaction-diffusion model. The reactive part of the reaction-diffusion equation is developed from a hot-spot mechanism, with a characteristic jump when φ passes the critical value φ c . Solving the stationary equation according to the Dirichlet boundary conditions, we find the ‘hot deals’ regions, meaning regions of speculative transactions which can be considered ‘dissipation’ as they do not contribute to the gross national product. The time propagation of these patterns in the one-dimensional space considered could explain the evolution of markets towards speculative bubbles. These are frequently met in the frame of emerging stock markets. Financial data, which illustrate the physical model refer to Romania's stock market, Bucharest S.E.

In the framework of the mathematically and conceptually simple two-level mean-field model of an electronic spin system characterised by the spin-lattice relaxation time, actual magnetic phenomena have been evaluated within the language of irreversible thermodynamics, namely in terms of internal entropy production. A suitable description of both reversible and irreversible magnetization processes is presented which enables one to distinguish between them. It is suggested that, on the basis of this model, the majority of the phenomena observed in magnetic systems, for example, the construction of hysteresis loops, the energy balance of magnetization processes, the Steinmetz rule, etc., should be experimentally evaluated.