**Preface to "Simulation with Entropy Thermodynamics"**

Entropy is the strange state function which extends the description of energy by adding to it the unique property in physics that is quality. Indeed, in addition to being quantified by the first law of thermodynamics, energy is qualified. Beyond this rather formal description, it is indeed on the emergence of a new tool that we should focus our attention. If, thanks to a variational principle, analytical mechanics triumphs in predicting the evolution of the systems it is able to describe, it nevertheless leaves aside whole sections of the description of processes, where the dispersion of energy and/or matter, in degrees of freedom made accessible, apparently makes it impossible to apply an extremal principle. It is here, with subtlety and elegance, that the entropic approach can be inserted. Whether it concerns the dimensioning of thermoelectric systems, the study of the stability of thermodynamic parameters, the out-of-equilibrium behavior of plasmas, or the transport of charge carriers in different states of matter, the entropic approach often proves to be the only closed relationship that allows us to understand the fate of a system in contact with a reservoir of matter and a reservoir of energy. The world of engineering has a lot of experience and pragmatism on these subjects, only a part of which has today found a fundamental analytical formulation. Far from claiming to answer the open-ended problems of maximizing or minimizing the production of entropy in a general framework, this book wants to offer the reader, through very different systems, a look at the different uses that can be made of entropy, as a measurement of the dispersion of energy and matter. This book brings together the variety of uses of entropy by its authors in their respective works. We would like to thank them all warmly for their work.

> **Christophe Goupil** *Editor*

*Article*

## **The Ohm Law as an Alternative for the Entropy Origin Nonlinearities in Conductivity of Dilute Colloidal Polyelectrolytes**

#### **Ioulia Chikina 1, Valeri Shikin 2 and Andrey Varlamov 3,\***


Received: 10 January 2020; Accepted: 13 February 2020; Published: 17 February 2020

**Abstract:** We discuss the peculiarities of the Ohm law in dilute polyelectrolytes containing a relatively low concentration *n*- of multiply charged colloidal particles. It is demonstrated that in these conditions, the effective conductivity of polyelectrolyte is the linear function of *n*-. This happens due to the change of the electric field in the polyelectrolyte under the effect of colloidal particle polarization. The proposed theory explains the recent experimental findings and presents the alternative to mean spherical approximation which predicts the nonlinear I–V characteristics of dilute colloidal polyelectrolytes due to entropy changes.

**Keywords:** polyelectrolytes; Ohm law; colloids
