Related papers: On Thermodynamic Interpretation of Copula Entropy
This is the monograph on the theory and applications of copula entropy (CE). This book first introduces the theory of CE, including its background, definition, theorems, properties, and estimation methods. The theoretical applications of CE…
Causal discovery is a fundamental problem in statistics and has wide applications in different fields. Transfer Entropy (TE) is a important notion defined for measuring causality, which is essentially conditional Mutual Information (MI).…
Identifying differential equation governing dynamical system is an important problem with wide applications. Copula Entropy (CE) is a mathematical concept for measuring statistical independence in information theory. In this paper we…
Variable selection is an important problem in statistics and machine learning. Copula Entropy (CE) is a mathematical concept for measuring statistical independence and has been applied to variable selection recently. In this paper we…
Time lag between variables is a key characteristics of dynamical systems in different fields and identifying such time lag is an important problem in complex systems with many applications. Transfer Entropy (TE) was proposed as a tool for…
Statistical independence and conditional independence are two fundamental concepts in statistics and machine learning. Copula Entropy is a mathematical concept defined by Ma and Sun for multivariate statistical independence measuring and…
In this paper we propose to apply copula entropy (CE) to facies classification. In our method, the correlations between geological variables and facies classes are measured with CE and then the variables associated with large negative CEs…
The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of…
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…
Electronic correlation is a fundamental topic in many-electron systems. To characterize this correlation, one may introduce the concept of exchange-correlation hole. In this paper, we first briefly revisit its definition and relation to…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
In various chemical systems enthalpy-entropy compensation (EEC) is a well-known rule of behavior, although the physical roots of it are still not completely understood. It has been frequently questioned whether EEC is a truly physical…
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…