Article

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

Journal of Statistical Mechanics Theory and Experiment (Impact Factor: 2.4). 01/2012; 2012(03). DOI: 10.1088/1742-5468/2012/03/P03002

Source: arXiv

**ABSTRACT**

The TASEP is a paradigmatic model from non-equilibrium statistical physics,

which describes particles hopping along a lattice of discrete sites. The TASEP

is applicable to a broad range of different transport systems, but does not

consider the fact that in many such systems the availability of resources

required for the transport is limited. In this paper we extend the TASEP to

include the effect of a limited number of two different fundamental transport

resources: the hopping particles, and the "fuel carriers", which provide the

energy required to drive the system away from equilibrium. As as consequence,

the system's dynamics are substantially affected: a "limited resources" regime

emerges, where the current is limited by the rate of refuelling, and the usual

coexistence line between low and high particle density opens into a broad

region on the phase plane. Due to the combination of a limited amount of both

resources, multiple phase transitions are possible when increasing the exit

rate beta for a fixed entry rate alpha. This is a new feature that can only be

obtained by the inclusion of both kinds of limited resources. We also show that

the fluctuations in particle density in the LD and HD phases are 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 severely

reduced.

which describes particles hopping along a lattice of discrete sites. The TASEP

is applicable to a broad range of different transport systems, but does not

consider the fact that in many such systems the availability of resources

required for the transport is limited. In this paper we extend the TASEP to

include the effect of a limited number of two different fundamental transport

resources: the hopping particles, and the "fuel carriers", which provide the

energy required to drive the system away from equilibrium. As as consequence,

the system's dynamics are substantially affected: a "limited resources" regime

emerges, where the current is limited by the rate of refuelling, and the usual

coexistence line between low and high particle density opens into a broad

region on the phase plane. Due to the combination of a limited amount of both

resources, multiple phase transitions are possible when increasing the exit

rate beta for a fixed entry rate alpha. This is a new feature that can only be

obtained by the inclusion of both kinds of limited resources. We also show that

the fluctuations in particle density in the LD and HD phases are 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 severely

reduced.

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