Multiple phase transitions in a system of exclusion processes with limited reservoirs ofparticles and fuel carriers

Abstract

The TASEP is a paradigmatic model from non-equilibrium statistical physics, whichdescribes particles hopping along a lattice of discrete sites. The TASEP is applicable to abroad range of different transport systems, but does not consider the fact that in manysuch systems the availability of resources required for the transport is limited. In this paperwe extend the TASEP to include the effect of a limited number of two differentfundamental transport resources: the hopping particles and the ‘fuel carriers’, whichprovide the energy required to drive the system away from equilibrium. As aconsequence, the system’s dynamics are substantially affected: a ‘limited resources’regime emerges, where the current is limited by the rate of refuelling, and theusual coexistence line between low and high particle density opens into a broadregion on the phase plane. Due to the combination of a limited amount of bothresources, multiple phase transitions are possible when increasing the exit rateβ for a fixedentry rate α. This is a new feature that can only be obtained by the inclusion of both kinds of limitedresources. We also show that the fluctuations in particle density in the LD and HD phasesare unaffected by fluctuations in the number of loaded fuel carriers, except by the fact that,when these fuel resources become limited, the particle hopping rate is severelyreduced.