Misuse of thermodynamic entropy in economics
We discuss a possibility of deriving an H-theorem for nonlinear discrete time evolution equation that describes random wealth exchanges. In such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a gas exchange their energy. It appears useful to reformulate the problem and represent the dynamics as a combination of two processes. The first is a linear transformation of a two-particle distribution function during the act of exchange while the second one corresponds to new random pairing of agents and plays a role of some kind of feedback control. This representation leads to a Clausius-type inequality which suggests a new interpretation of the exchange process as an irreversible relaxation due to a contact with a reservoir of a special type. Only in some special cases when equilibrium distribution is exactly a gamma distribution, this inequality results in the H-theorem with monotonically growing ‘entropy’ functional which differs from the Boltzmann entropy by an additional term. But for arbitrary exchange rule the evolution has some features of relaxation to a non-equilibrium steady state and it is still unclear if any general H-theorem could exist.
A vocationally-oriented course on Physics with medico-biological direction is proposed in this book. The matters of application of physical methods for substances investigation are considered here in detail.
The book may ne helpful for students of medical and pharmaceutical institutes of higher education and colleges, chemical, biological and pharmaceutical faculties of universities, as well as for students of core classes and teachers of medico-biological specialties.
Conformance checking is a subarea of process mining that studies relations between designed processes, also called process models, and records of observed processes, also called event logs. In the last decade, research in conformance checking has proposed a plethora of techniques for characterizing the discrepancies between process models and event logs. Often, these techniques are also applied to measure the quality of process models automatically discovered from event logs. Recently, the process mining community has initiated a discussion on the desired properties of such measures. This discussion witnesses the lack of measures with the desired properties and the lack of properties intended for measures that support partially matching processes, i.e., processes that are not identical but differ in some steps. The paper at hand addresses these limitations. Firstly, it extends the recently introduced precision and recall conformance measures between process models and event logs that possess the desired property of monotonicity with the support of partially matching processes. Secondly, it introduces new intuitively desired properties of conformance measures that support partially matching processes and shows that our measures indeed possess them. The new measures have been implemented in a publicly available tool. The reported qualitative and quantitative evaluations based on our implementation demonstrate the feasibility of using the proposed measures in industrial settings.
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy-power inequality for the weighted entropy and discuss connections with weighted Lieb’s splitting inequality. The concepts of rates of the weighted entropy and information are also discussed.