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The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
This work's purpose is to understand the dynamics of some social systems whose properties can be captured by certain iterated function systems. To achieve this intension, we start from the theory of iterated function systems, and then we…
We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a…
Nonlinear constrained optimization problems are encountered in many scientific fields. To utilize the huge calculation power of current computers, many mathematic models are also rebuilt as optimization problems. Most of them have…
Recent research on mobile robots has focused on increasing their adaptability to unpredictable and unstructured environments using soft materials and structures. However, the determination of key design parameters and control over these…
A thermodynamic approach to the description of economic systems and processes is developed. It is shown that there is a deep analogy between the parameters of thermodynamic and economic systems (markets); so each thermodynamic parameter can…
Modular design maximizes utility by using standardized components in large-scale systems. From a manufacturing perspective, it supports green technology by reducing material waste and improving reusability. Industrially, it offers economic…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this…
Economics has long been a science of static equilibria, in which time is a second-order rather than first-order concern. Without time, economic modelers may neglect or obscure the role of time-dependent phenomena, e.g. path-dependency, and…
Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the…
In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
The sum-utility maximization problem is known to be important in the energy systems literature. The conventional assumption to address this problem is that the utility is concave. But for some key applications, such an assumption is not…
Students of Computer Science often wonder when, exactly, one can apply a greedy algorithm to a problem, and when one must use the more complicated and time-consuming techniques of dynamic programming. This paper argues that the existing…
This paper develops a new model of business cycles. The model is economical in that it is solved with an aggregate demand-aggregate supply diagram, and the effects of shocks and policies are obtained by comparative statics. The model builds…
The algebra of transactions as fundamental measurements is constructed on the basis of the analysis of their properties and represents an expansion of the Boolean algebra. The notion of the generalized economic measurements of the economic…
Natural resource use and waste production, disposal, and reuse in human economies are treated in their economic, technological and thermodynamic aspects. The physical nature of economic production, consumption, saving, and waste is compared…
Systemic risk is a rapidly developing area of research. Classical financial models often do not adequately reflect the phenomena of bubbles, crises, and transitions between them during credit cycles. To study very improbable events,…