Entropy behavior for isolated systems containing bounded and unbounded states: latent heat at the inflection point

Abstract

Systems like the Morse oscillator with potential energies that have a minimum and states that are both bounded and extended are considered in this study in the microcanonical statistical ensemble. In the binding region, the entropy becomes a growing function of the internal energy and has a well-defined inflection point corresponding to a temperature maximum. Consequently, the specific heat supports negative and positive values around this region. Moreover, focusing on this inflection point allows to define the critical energy and temperature, both evaluated analytically and numerically. Specifically, the existence of this point is the signature of a phase transition, and latent heat dynamics occur to accomplish the transition. The conditions established below apply to a large variety of potentials, including molecular ones, and have relevance for physics, chemistry, and engineering sciences. As a specific application, we show that the inflection point for the H 2 molecule occurs at −1.26 [eV]. NomenclatureA Energy parameter defining the potential a -1

Transition Temperature of Color Change in Thermochromic Systems and Its Description Using Sigmoidal Models

“…The thermochromic color change in thermochromic inks containing dye and developer is characterized using a sigmoid transition along with an inflection point, as is the case with many other phase transitions [37][38][39][40]. A frequently used function in this case is the sigmoidal function proposed by Boltzmann (1879) [37], which has the following univariate binary form: y = 1/(1 + e x ).…”

“…The thermochromic color change in thermochromic inks containing dye and developer is characterized using a sigmoid transition along with an inflection point, as is the case with many other phase transitions [37][38][39][40]. A frequently used function in this case is the sigmoidal function proposed by Boltzmann (1879) [37], which has the following univariate binary form: y = 1/(1 + e x ). In our case, we used a modified version that allows us to determine the inflection point of the color transition and temperature distances (the difference between the temperature at which the color change of the thermochromic system begins and the temperature at which it ends).…”