Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect

This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and shows their connection with the formalism of kappa distributions. By defining the “entropy defect” in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm.

Algorithms for monitoring the functioning of nonequilibrium information processing systems

The authors have developed an algorithm for monitoring the functioning of nonequilibrium systems, which is based on such operations as establishing the range for permissible values of efficiency probabilities of structural elements functioning, establishing permissible values of structural elements amount, plotting the system entropy dependence on structural elements amount and their effectiveness probability, constructing phase space of the system functioning and determination of the boundaries of regions with nonequilibrium stability. Practical testing of the developed algorithm for monitoring the functioning of nonequilibrium systems has shown that this algorithm can be used to solve several practical problems related to functioning monitoring and predicting the state of a wide variety of nonequilibrium systems.

Understanding entropy

A new way of understanding entropy as a macroscopic property is presented. This is based on the fact that heat flows from a hot body to a cold one even when the hot one is smaller and has less energy. A quantity that determines the direction of flow is shown to be the increment of heat gained (q) divided by the absolute temperature (T). The same quantity is shown to determine the direction of other processes taking place in isolated systems provided that q is determined by the state (s) of the system. Entropy emerges as the potent energy of a system [Σ(qs/T)], the potency being determined by 1/T. This is shown to tie in with the statistical mechanical interpretation of entropy. The treatment is shorter than the traditional one based on heat engines.

Page curve from non-Markovianity

In this paper, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.

Anomalous Thermopower and High ZT in GeMnTe2 Driven by Spin’s Thermodynamic Entropy

NaxCoO2 was known 20 years ago as a unique example in which spin entropy dominates the thermoelectric behavior. Hitherto, however, little has been learned about how to manipulate the spin degree of freedom in thermoelectrics. Here, we report the enhanced thermoelectric performance of GeMnTe2 by controlling the spin’s thermodynamic entropy. The anomalously large thermopower of GeMnTe2 is demonstrated to originate from the disordering of spin orientation under finite temperature. Based on the careful analysis of Heisenberg model, it is indicated that the spin-system entropy can be tuned by modifying the hybridization between Te-p and Mn-d orbitals. As a consequent strategy, Se doping enlarges the thermopower effectively, while neither carrier concentration nor band gap is affected. The measurement of magnetic susceptibility provides a solid evidence for the inherent relationship between the spin’s thermodynamic entropy and thermopower. By further introducing Bi doing, the maximum ZT in Ge0.94Bi0.06MnTe1.94Se0.06 reaches 1.4 at 840 K, which is 45% higher than the previous report of Bi-doped GeMnTe2. This work reveals the high thermoelectric performance of GeMnTe2 and also provides an insightful understanding of the spin degree of freedom in thermoelectrics.

Decision Making in IoT Systems Based on Guided Self-Organization and Autonomic Computing in the Context of the I4.0 Era

Internet of things (IoT) systems are taking an important role in daily life. Each year the number of connected devices increases considerably, and it is important to keep systems working appropriately. There are some options related to decision support systems to perform IoT systems tasks such as deployment, maintenance, and its operation on environments full of different connected devices and IoT systems interacting among them. For the decision-making process, the authors consider the complexity nature observed in IoT systems and their operational context and environments. In this sense, rather than using grain and fixed control rules/laws for the system design, the use of general principles, goals, and objectives are defined to guide the system adaptation. This has been referred to as guided self-organization (GSO) in the literature. The GSO design approach is based in evaluating the system entropy to reduce the emergence and enable self-organization. Also, in this chapter, a series of study cases from different IoT application domains are presented.

Bijective model of time and J.T. Fraser’s Nowless Universe

In bijective modelling, the physical reality is represented by the set X, the model of physical reality by the set Y. Every element in the set X has exactly one correspondent element in the set Y. Set X and set X are related by the bijective function f:X→Y. Bijective modelling is confirming that time is the duration of given system entropy increasing in time-invariant space. Time-invariant space is the fundamental arena of the Nowless Universe.

Magnetization and Magnetocaloric Effect in Antiferromagnets with Competing Ising Exchange and Single-Ion Anisotropies

The magnetization of a two-sublattice Ising antiferromagnet with easy-plane single-ion anisotropy, which is accompanied by two phase transitions, has been studied. The both phase transitions are induced by the magnetic field. One of them is isostructural, i.e., the system symmetry remains unchanged and a transition between two antiferromagnetic states with different sublattice magnetizations takes place. The other phase transition occurs when the antiferromagnetic state transforms into the ferromagnetic one. At both phase transitions, the field dependence of the system entropy has two successive positive jumps, which is not typical of ordinary antiferromagnets. On the other hand, if the temperature of the system is higher than the tricritical temperature of the isostructural phase transition, there appears a continuous maximum in the field dependence of the entropy.