Volume 49, Issue 2 - Special Issue: The 17th Joint European Thermodynamics Conference (JETC 2023); Guest Editors: Vito Antonio Cimmelli and Antonio Sellitto

In recent years, great efforts are devoted to reducing the work cost of the bit operation, but it is still unclear whether these efforts are sufficient for resolving the temperature stabilization problem in computation. By combining information thermodynamics and a generalized constitutive model which can describe Fourier heat conduction as well as non-Fourier heat transport with nonlocal effects, we here unveil two types of the thermodynamic costs in the temperature stabilization problem. Each type imposes an upper bound on the amount of bits operated per unit time per unit volume, which will eventually limit the speed of the bit operation. The first type arises from the first and second laws of thermodynamics, which is independent of the boundary condition and can be circumvented in Fourier heat conduction. The other type is traceable to the third law of thermodynamics, which will vary with the boundary condition and is ineluctable in Fourier heat conduction. These thermodynamic costs show that reducing the work cost of the bit operation is insufficient for resolving the temperature stabilization problem in computation unless the work cost vanishes.

Over the last twenty-five years, the search for generalized equations that allow us to better understand the phenomenon of heat conduction has become an active frontier both in transport theory, and in non-equilibrium thermodynamics, due to the growing interest in nanotechnologies, thermal metamaterials and fast devices. Here we review how some mathematical analogies between generalized heat-transport equations and well-known equations in hydrodynamics, electronics and optics have been helpful to infer new forms of heat transfer arising in extended thermodynamics and to inspire the consideration of new phenomena. We also examine in each case the thermodynamic basis of the respective formulation.

The JETC Conference held in Salerno (June 12–17, 2023) was the opportunity to honor the two centuries anniversary of the booklet publication of Sadi Carnot. The paper reports on a selective review summarizing the evolution of the ideas and concepts proposed by Carnot. We consider mainly: a. The Carnot cycle relative to thermomechanical engine, b. The concept of efficiency (Carnot efficiency), c. The forms of energy (thermal energy or heat, Q , and mechanical energy or work, W ), d. The concept of entropy, rediscovered and completed by Clausius. We show the importance of the energy conversion irreversibilities that started to be considered more recently by two methods, namely, the ratio method and the entropy production method. The second approach provides more significant results from a global point of view, also with more local modeling (cycle process modeling). Some examples are given that illustrate the proposal: Carnot cycle in endo-irreversible or exo-reversible configuration, Chambadal modeling, Curzon–Ahlborn modeling. More generally, the modeling is done in the frame of FTT (Finite Time Thermodynamics), FST (Finite Speed Thermodynamics), or FDOT (Finite physical Dimensions Optimal Thermodynamics). Preliminary conclusions and perspectives are proposed.

The development of non-Fourier heat conduction models is encouraged by the invalidity of Fourier’s law to explain heat conduction in ultrafast or ultrasmall systems. The production of negative entropy will result from the combination of traditional nonequlibrium thermodynamics and non-Fourier heat conduction models. To resolve this paradox, extended irreversible thermodynamics (EIT) introduces a new state variable. However, real dynamics variables like force and momentum are still missing from nonequilibrium thermodynamics and EIT’s generalized force and generalized flux. Heat has both mass and energy, according to thermomass theory and Einstein’s mass-energy relation. The generalized heat conduction model containing non-Fourier effects was established by thermomass gas model. The thermomass theory reshapes the concept of the generalized force and flux, temperature, and entropy production in nonequilibrium thermodynamics and revisits the assumption for the linear regression of the fluctuations in Onsager reciprocal relation. The generalized heat conduction model based on thermomass theory has been used to study thermal conductivity, thermoelectric effect, and thermal rectification effect in nanosystems.

Determining the thermal properties of materials with complex structures is still a major engineering challenge today. The well-known heat pulse experiment can be used to determine the thermal diffusivity by measuring the temperature history as a thermal response for a fast excitation. However, the evaluation of the measurements can be challenging, especially when dealing with non-homogeneous samples. The thermal behavior of such heterogeneous materials may exhibit a response including two-time scales. Therefore, the Fourier equation is not necessarily applicable. The simplest possible alternatives are the 2-temperature models the Guyer–Krumhansl and Jeffreys heat equations. In the present paper, we focus on the interpretation of the Jeffreys heat equation; studying its analytical solution, we present a fitting method for determining the unknown parameters. We also discuss its relation with the other two heat equations, and we offer an interpretation of how to characterize the transient response of heterogeneous materials.

The consequences of introducing the fourth order orientation tensor as an independent variable in addition to the second order one are investigated. In the first part consequences of the Second Law of Thermodynamics are exploited. The cases with the second order alignment tensor in the state space on one hand and with the second and fourth order alignment tensors on the other hand are analogous. In the latter case differential equations for the second and fourth order tensors result from linear force-flux relations with a coupling arising due to coupling terms in the free energy. In the second part the differential equations for the second order orientation tensor or the second and fourth order orientation tensors, respectively are given explicitly in the special case of a rotation symmetric orientation distribution. The Folgar-Tucker equation with a quadratic closure relation leads to a Riccati equation for the second order parameter. In comparison the Folgar-Tucker equation and the differential equation for the fourth order parameter are considered. The fourth order parameter is eliminated later. The resulting equation for the second order parameter is a Duffing equation with a behavior of solutions completely different from the solutions of the Riccati equation.

Even when microscopic particle dynamics is purely mechanistic and thus reversible, the behavior of macroscopic systems composed of those particles is irreversible. In other words, effectively irreversible behavior emerges out of purely reversible dynamics when we do not observe all degrees of freedom of the detailed dynamics. But how can we find the irreversible macroscopic evolution equations when we only know the reversible microscopic equations? Using the so-called lack-of-fit reduction, which gives the reduced evolution as a sum of Hamiltonian and gradient dynamics, we reduce the purely Hamiltonian Kac–Zwanzig model to a set of irreversible evolution equations with no fitting parameters.

The main aim of this work is to optimize a Quantum Drift Diffusion model (QDD) (V. Romano, M. Torrisi, and R. Tracinà, “Approximate solutions to the quantum drift-diffusion model of semiconductors,” J. Math. Phys. , vol. 48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, “Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model,” SIAM J. Appl. Math. , vol. 66, no. 2, pp. 554–572, 2005; L. Barletti and C. Cintolesi, “Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics,” J. Stat. Phys. , vol. 148, pp. 353–386, 2012) by comparing it with the Boltzmann-Wigner Transport Equation (BWTE) (O. Muscato, “Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode,” J. Comput. Electron ., vol. 20, pp. 2062–2069, 2021) solved using a signed Monte Carlo method (M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, “Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices,” Phys. Rev. B , vol. 70, pp. 115–319, 2004). A situation of high non equilibrium regime is investigated: electron transport in a Resonant Tunneling Diode (RTD) made of GaAs with two potential barriers in GaAlAs. The range of the suitable voltage bias applied to the RTD is analyzed. We find an acceptable agreement between QDD model and BWTE when the applied bias is low or moderate with a threshold of about 0.225 V over a length of 150 nm; it is found out that the use of a field dependent mobility is crucial for getting a good description of the negative differential conductivity in such a range. At higher bias voltages, we expect that QDD model loses accuracy.

In this paper, we study the influence of the boundary conditions of the velocity fields in superfluid helium counterflow experiments. To make progress, we perform numerical simulations where we allow a slip velocity of the viscous component at the walls, and observe how this impacts on velocity fields and density profiles of distribution of quantized vortices. We conclude that the presence of a slip velocity at the walls generates a more homogeneous vortex distribution throughout the channel.

We review models for convective motion which have a flux law of Cattaneo type. This includes thermal convection where the heat flux law is a Cattaneo one. We additionally analyse models where the convective motion is due to a density gradient caused by a concentration of solute. The usual Fick’s law in this case is replaced by a Cattaneo one involving the flux of solute and the concentration gradient. Other effects such as rotation, the presence of a magnetic field, Guyer–Krumhansl terms, or Kelvin–Voigt theories are briefly introduced.

The modeling and understanding of micro- and nano-scale transport processes have raised increasing attention and extensive investigation during the past decades. In this mini-review, we aim to summarize our recent progress on the non-equilibrium thermodynamics of micro- and nano-scale flow and heat transfer. Special emphasis is put on the entropy generation at the interface, which plays a dominant role at small scale due to the strong non-equilibrium nature of particle-boundary interaction. We also prove the thermodynamic compatibility of both the macroscopic hydrodynamic equation and the non-equilibrium boundary conditions from the perspective of bulk and interfacial entropy generations respectively, as supported by the kinetic theory of microscopic particles. The present review will contribute to a clearer elaboration of thermodynamics at micro/nano-scale and its statistical mechanical demonstration, and thus will promote its further development in the future.

Employing the Laplace transform and its properties, we investigate the evolution of the coupled thermal and fluid-acoustic waveforms that arise in a signaling problem under the Eringen–Cattaneo–Christov–Straughan model of poroacoustic phenomena. Assuming a Heaviside temperature input, we determine the effects of what we term the “Eringen coefficient” by examining the propagation and evolution of the resulting shock and/or acceleration waveforms. Special/limiting cases are also discussed and, in the final section of this Note, possible follow-on studies are suggested.