2007/11/30 by A. Rákos, A Rákos, R. J. Harris +1 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/2008/05/p05005
published as Journal of Statistical Mechanics: Theory and Experiment 2008, P05005 · 37 pages, 10 figures. Minor alterations, fixed typos (as appeared in JSTAT)
openalex publication_date 2008/05/12 · arxiv created 2008/06/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 (Harris et al 2006 Europhys. Lett. 75 227) 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 Giardinà et al (2006 Phys. Rev. Lett. 96 120603), 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.