Takahiro Nemoto
Title
Computation of Large Deviation Statistics via Iterative
Measurement-and-Feedback Procedure
Abstract
Thermodynamic functions give relations between some macroscopic
observables to other observables in equilibrium system. The functions are constructed by operational or phenomenological manners within the theory of thermodynamics. On the other side, from the statistical mechanics, which connects the thermodynamic functions to microscopic descriptions like Newtonian dynamics, it has been known that the thermodynamic functions also have played a role as the large deviation functions of thermodynamic variables. The structure is suggestive, and recently, there has been several studies to extend this structure to the large deviation functions of time-averaged quantities in non-equilibrium systems.
In time-series statistics, the large deviation function gives a frequency of rare events in quantitative manner. Then, what follows from a phenomenology, which allows us to measure the large deviation function with an operational manner, if it exists? On one hand, the large deviation function is phenomenologically obtained. On the other hand, it describes the frequency of rare events characterized by large deviation principle.
Such a phenomenology may become a rare event sampling method that can be used for real experiments. In this talk, towards this goal, we propose a method to compute large deviation functions of time-averaged quantity in operational manner [T. N. and S. Sasa, PRL. 112, 090602 (2014)]. The method is composed of an iteration of a measurement and feedback procedure that can be implemented in real experiment in principle. We apply the method to numerical simulations of non-equilibrium lattice gases, and show some non-trivial features about rare events behind those models.