Microscopic fluctuation theory (mFT) for interacting Poisson processes. (English) Zbl 1507.82058
Summary: While the macroscopic fluctuation theory is a renormalized theory in the hydrodynamic limit based on a space-time local Lagrangian that is Gaussian with respect to the empirical current, C. Maes et al. [Markov Process. Relat. Fields 14, No. 3, 445–464 (2008; Zbl 1156.82360)] have derived a microscopic fluctuation theory for independent Markov jump processes based on a space-time local Lagrangian that is Poissonian with respect to the empirical flow, in direct relation with the general theory of large deviations at ‘Level 2.5’ for Markovian processes. Here we describe how this approach can be generalized to the presence of interactions, that can be either zero-range or involve neighbors, either for closed systems or for open systems with reservoirs.
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 60F10 | Large deviations |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 60J27 | Continuous-time Markov processes on discrete state spaces |
Citations:
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