Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process

Abstract

The Giardinà-Kurchan-Peliti algorithm is a numerical procedure that uses population dynamics in order to calculate large deviation functions associated to the distribution of time-averaged observables. To study the numerical errors of this algorithm, we explicitly devise a stochastic birth-death process that describes the time evolution of the population probability. From this formulation, we derive that systematic errors of the algorithm decrease proportionally to the inverse of the population size. Based on this observation, we propose a simple interpolation technique for the better estimation of large deviation functions. The approach we present is detailed explicitly in a two-state model.

13 pages, 1 figure. First part of pair of companion papers, Part II being arXiv:1607.08804

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• Universality in dynamical phase transitions of diffusive systems
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• Finite time large deviations via matrix product states
• Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions: Numerical Approach in Continuous Time
• Methods and Conversations in (Post)Modern Thermodynamics
• Transport Coefficients from Large Deviation Functions
• Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems
• Spectral properties of the trap model on sparse networks
• Rare event simulation for stochastic dynamics in continuous time
• Approaching a large deviation theory for complex systems
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• Dynamical phase transitions for the activity biased Ising model in a magnetic field
• Stochastic formalism for thermally driven distribution frontier: A nonempirical approach to the potential escape problem
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• Effective bandwidth of non-Markovian packet traffic
• Computing large deviation rate functions of entropy production for diffusion processes by an interacting particle method