Stochastic fluctuations as a driving force to dissipative non-equilibrium states

Abstract

Abstract Most natural complex systems exhibit fluctuations-driven processes, which work at far from equilibrium states, and are generally dissipative processes, for instance living cells. We studied this phenomenon within the stochastic framework by taking a set of nonequilibrium, bimolecular, autocatalytic reactions, originally proposed by Nicolis (1972). We also extended this model to incorporate the concept of time delay. Firstly, for both non-delay and delay cases, we calculated the exact non-stationary probability distribution solutions of the corresponding Master equations, which are found to deviate from the Maxwell–Boltzmann distribution. The analytically calculated probability distribution P of an autocatalyst X in the chemically reacting model system is found to follow some universal class of probability distributions at different situations. At the thermodynamic limit with a large population, P obeys Normal distribution. Again, we showed that one of the causes of this peculiar behaviour is the fluctuations in the reacting system. The analytical result of the Fano factor F in the non-delay case predicted a noise-enhanced process for our dynamical stochastic system which could probably drive the system far from equilibrium. For the delay case, the analytically calculated F was found to depend on the time delay function, which predicts that time delay could play an important role in regulating the system dynamics. These analytical predictions were then verified using numerical experiments with the stochastic simulation algorithm (SSA) and delay stochastic simulation algorithm (DSSA). Indeed, numerical results from SSA and DSSA confirmed noise-enhanced processes which are far from equilibrium and dissipative in nature.