Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-11-21
Journal of Statistical Mechanics: Theory and Experiment 2008, P05005
Physics
Condensed Matter
Statistical Mechanics
37 pages, 10 figures. Minor alterations, fixed typos (as appeared in JSTAT)
Scientific paper
10.1088/1742-5468/2008/05/P05005
We consider the fluctuations of generalized currents in stochastic Markovian dynamics. The large deviations of current fluctuations are shown to obey a Gallavotti-Cohen (GC) type symmetry in systems with a finite state space. However, this symmetry is not guaranteed to hold in systems with an infinite state space. A simple example of such a case is the Zero-Range Process (ZRP). Here we discuss in more detail the already reported breakdown of the GC symmetry in the context of the ZRP with open boundaries and we give a physical interpretation of the phases that appear. Furthermore, the earlier analytical results for the single-site case are extended to cover multiple-site systems. We also use our exact results to test an efficient numerical algorithm of Giardina, Kurchan and Peliti, which was developed to measure the current large deviation function directly. We find that this method breaks down in some phases which we associate with the gapless spectrum of an effective Hamiltonian.
Harris Robert J.
Rákos Attila
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