Abstract
We study conserved stochastic sandpiles (CSSs), which exhibit an active-absorbing phase transition upon tuning density . We demonstrate that a broad class of CSSs possesses a remarkable hydrodynamic structure: There is an Einstein relation , which connects bulk-diffusion coefficient , conductivity , and mass fluctuation, or scaled variance of subsystem mass, . Consequently, density large-deviations are governed by an equilibrium-like chemical potential , where is the activity in the system. By using the above hydrodynamics, we derive two scaling relations: As , being the critical density, (i) the mass fluctuation with and (ii) the dynamical exponent , expressed in terms of two static exponents and for activity and correlation length , respectively. Our results imply that conserved Manna sandpile, a well studied variant of the CSS, belongs to a distinct universality—not that of directed percolation (DP), which, without any conservation law as such, does not obey scaling relation (ii).
- Received 18 September 2017
- Revised 22 December 2017
DOI:https://doi.org/10.1103/PhysRevE.97.062142
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