Special Session 68: Entropy-Like Quantities and Applications

Entropy is a general concept that appears in different settings with different meanings. Thus, it measures disorder in physics, uncertainty in information theory, minimum code length in coding theory, (pseudo-)randomness in measure-preserving dynamical systems, complexity in topological dynamics, and algorithmic complexity in computer science. As for its importance, let us remind that it enters the second axiom of thermodynamics, related to the direction of time in many-particle mechanical systems. In information theory it defines the very concept of information, beside lying at the core of the fundamental results. And, last but not least, in ergodic theory entropy is perhaps the most important invariant of metric and topological conjugacy, which are the equivalence concepts in measure-preserving and topological dynamics, respectively. In the last decades new versions of entropy has come to the fore. Sequence entropy, correlation entropy, permutation entropy, transfer entropy, approximate entropy, sample entropy, etc. are some of the entropy-like quantities proposed by researchers to cope with new challenges in ergodic theory, chaos, synchronization and control, information theory, time series analysis, etc. Along with these new developments, some traditional topics, like the computation (and even computability) of metric and topological entropy, still remain the subject of current research in applied mathematics. Also in physics, entropy is the objective of undiminished research activity, topics ranging from axiomatic aspects to its formulation in non-stationary processes. This Special Session is organized with the scope that researchers on the theoretical or practical aspects of entropy and akin quantities can share their interests and latest results in a multidisciplinary environment. Therefore, participants from all fields of science, mathematics and engineering are very much welcome.