ABSTRACT
Understanding the kinetics of electron transfer reactions involves active research in physics, chemistry, biology, and nano-tech. Here, we propose a model to apply in a broader framework by establishing a connection between thermodynamics and kinetics. From a purely thermodynamic point of view, electronic transfer Marcus' theory is revisited; consequently, calculations of thermodynamic variables such as mobility, energy, and entropy are provided. More significantly, two different regimes are explicitly established. In the anomalous region, an exergonic process associated with negative heat capacity appears. Further, in the same region, mobility, energy, and entropy decrease when the temperature increases.
ABSTRACT
In this paper, we study a finite direct electrical transmission line when we distribute resistors R_{n} according to a parity-time (PT) distribution composed of a gain (-R) and loss (+R) sequence. Considering zero boundary conditions, we find analytical results for the frequency spectrum ω(R,k_{d}) as a function of resistance R and the wave number k_{d}. A frequency spectrum analysis shows a phase transition from real to complex eigenvalues as a function R for fixed k_{d=N}, where 2N is the size of the transmission line. Numerically, we study localization properties through the normalized localization length Λ(R,k_{d}). This measure shows good agreement with the analytical results and gives an account of the PT-phase transition. Our results pave a solid way toward studying the interplay between parity-time symmetry concepts and one-dimensional electrical transmission lines, aiming to find another generation of electronic devices capable of controlling the flow of energy.