This paper provides a concise overview of three current and very active frontiers of the second law of thermodynamics; namely, non-equilibrium macroscopic systems, mesoscopic systems, and systems with quantum correlations. Rather than providing an extensive review of this very wide topic, we sketch some views on the basic ideas of several current explorations of the limits of the second law. Furthermore, we emphasise the relevance of a suitable definition of temperature in non-equilibrium situations to avoid some apparent paradoxes arising in Carnot cycles with driven heat reservoirs with quantum correlations.
In a recent paper the authors proved that the dispersion relation of heat waves along nanowires could allow one to illustrate the difference between different definitions of non-equilibrium temperature. It turns out that, from the practical perspective, one is led to the same conclusions by using both the absolute non-equilibrium temperature and a dynamical non-equilibrium temperature. Starting from these results, in the present paper the propagation of heat waves in core-shell nanowires is analyzed by using the concept of absolute non-equilibrium temperature. It is shown how the wave speed depends on the properties of both media and on their mutual interaction. Some useful information about the system is presented.
A model for semiconductor crystals and superlattices with dislocations proposed in a previous paper is used here to study the thermal, electrical and mechanical properties of these defective materials. The standard procedures of non-equilibrium thermodynamics with internal variables are applied to derive in the linear approximation constitutive equations as well as rate equations for the dislocation, charges and heat flux fields, containing coupled effects among the different fields. A new dislocation tensor is used to describe the geometry of the dislocation lines, because their relative orientation with respect to the superlattice interfaces is very relevant.
We provide an overview on the problem of modeling heat transport at nanoscale and in far-from-equilibrium processes. A survey of recent results is summarized, and a conceptual discussion of them in the framework of Extended Irreversible Thermodynamics is developed.
We propose a description of heat conduction in rigid solids in which the classical state space of extended thermodynamics is substituted with another one, spanned by a dynamical semi-empirical temperature and a renormalized flux variable, given by the thermodynamic conjugate of the heat flux and proportional to the heat relaxation time and the dynamical temperature gradient. Propagation of heat pulses in dielectric crystals at low temperatures is analyzed, and the results are compared with those obtained by Lebon et al. (J. Phys.: Condens. Matter, 20 (2008), 025223). We propose a possible experiment in order to check what is the most well-suited definition of temperature in non-equilibrium situations.
We develop a mesoscopic model of thermoelectric coupling in nanosystems, allowing for different phonon and electron temperatures, and mutual energy exchange. Its compatibility with the second law of thermodynamics is proved. By comparisons with other theoretical proposals, the different coefficients involved in the model are identified. We consider two illustrations: (a) for systems where the electron mean-free path is considerably shorter than the phonon mean-free path, the non-equilibrium phonon temperature may be different with respect to the local-equilibrium temperature of electrons; (b) for systems with large electron mean-free path, one may have the so-called “hot electrons,” namely, electrons having a higher temperature than that of the phonons.
Curved interfaces between material media with different characteristic speed for heat waves may be the basis for thermal lenses, concentrating the energy carried by parallel thermal rays on a focal point. This may be of practical use for the amplification of thermal signals and for the development of sensitive thermal sensors. When dissipative attenuation effects are taken into account, it turns out that these lenses could be of special interest in miniaturized probes, or in micro/nanosystems, and the optimization of the thermal lens for signal amplification may be calculated.