ABSTRACT
In chaos theory, little attention has been paid to energy dissipation and its fluctuation [1] in the dynamical systems approach, while there are important theorems such as Nyquist theorem and Onsager’s theorem in the traditional statistical mechanics [2-4]. Rather, the main part of chaos theory covers the universal features of bifurcations, structure of strange attractor and various kinds of universality in deterministic chaos in the dissipative dynamical systems [5-8]. It might seem curious that the dissipation and fluctuation problems do not enter the dynamical laws of chaos theory. However, it may be very natural as only the dynamics of macroscopic physical quantities are treated and one can only find the deterministic nature of the dynamical systems from chaos theory. In nonlinear dynamical systems, there apparently exists time’s arrow or the broken time-reversal symmetry which is tightly related to the cooperative phenomenon and the energy dissipation among a huge number of molecules [9]. So, more precisely, it may be true to say that spatially extended dynamical systems with infinite degrees of freedom are also ruled by energy dissipation and fluctuation. If the dissipation rate (or energy) is known or defined adequately in a nonlinear dynamical system, one can argue chaotic fluctuation from the viewpoint of the dissipation/ fluctuation problem. Here the semiconductor chaos system is presented from a new approach given by Mori et al. [1]. In semiconductors the dissipation energy is well known, so that the argument seems to be more realistic than many other dynamical systems. The approach [1] is an extended version of a statistical-mechanical formalism which characterizes globally the chaotic fluctuation by the coarse-grained divergence rate of nearby orbits [10, 11]. The q-phase transition found by the statisticalmechanical formalism is also supplemented here.
