Related papers: Group structure as a foundation for entropies
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
We consider here a class of groupoids obtained via an equivalence relation (the subgroupoids of pair groupoids). We generalize to Haar Systems in these groupoids some results related to entropy and pressure which are well known in…
We first present open questions related to the foundations of thermodynamics and statistical physics. We then argue that in principle one can not have "closed systems", and that a universal background should exist. We propose that the…
We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy…
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
We give the basic definition of algebraic entropy for lattice equations. The entropy is a canonical measure of the complexity of the dynamics they define. Its vanishing is a signal of integrability, and can be used as a powerful…
Epistasis is a key concept in the theory of adaptation. Indicators of epistasis are of interest for large system where systematic fitness measurements may not be possible. Some recent approaches depend on information theory. We show that…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
The reasons for introducing the concept of the entrostat in statistical physics are examined. The introduction of the concept of the entrostat has allowed to show the possibility of self-organization in open systems within the understanding…
This short book is an elementary course on entropy, leading up to a calculation of the entropy of hydrogen gas at standard temperature and pressure. Topics covered include information, Shannon entropy and Gibbs entropy, the principle of…
We partially generalize Peters' formula on modules over the group ring ${\mathbb F} \Gamma$ for a given finite field ${\mathbb F}$ and a sofic group $\Gamma$. It is also discussed that how the values of entropy are related to the zero…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
We define the notion of entropy for a cross section of an action of continuous amenable group and relate it to the entropy of the ambient action. As a result, we are able to answer a question of J.P. Thouvenot about completely positive…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
The recursive property of entropy is well known in information theory; however, the concept is underutilized in thermodynamics, despite being the field where the concept of entropy originated. The zentropy approach is built on this idea,…
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
In order to apply thermodynamics to systems in which entropy is not extensive, it has become customary to define generalized entropies. While this approach has been effective, it is not the only possible approach. We suggest that some…
Algebraically, entropy can be defined for abelian groups and their endomorphisms, and was latter extended to consider objects in a Flow category derived from abelian categories, such as $R\textit{-}Mod$ with $R$ a ring. Preradicals are…