Occupation-time statistics of a gas of interacting diffusing particles

Abstract

The time which a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently the joint occupation time statistics of an ensemble of non-interacting particles was addressed using the single-particle statistics. Here we employ the Macroscopic Fluctuation Theory (MFT) to study the occupation time statistics of many interacting particles. We find that interactions can significantly change the statistics and, in some models, even cause a singularity of the large-deviation function describing these statistics. This singularity can be interpreted as a dynamical phase transition. We also point out to a close relation between the MFT description of the occupation-time statistics of non-interacting particles and the level 2 large deviation formalism which describes the occupation-time statistics of a single particle.

Large Deviations Conditioned on Large Deviations II: Fluctuating Hydrodynamics

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“…[ρ] at three different times of the evolution, namely, at t = 0, at t = T , and in the quasi-stationary regime. These are, in general, related by (see (27))…”

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Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations

“…Using MFT, it was understood that for many non-equilibrium systems the probability density is highly non-trivial. For example, the probability distribution of the density field is generically a non-local functional of the field and the probability distributions of various quantities are often singular [24][25][26][27][28][29][30][31]. To date, an analogous set of results for active matter systems does not exist.…”

Diffusion and entanglement in open quantum systems

“…It is a complete hydrodynamic theory that captures the full range of non-equilibrium phenomena through the diffusion coefficient (density dependent function in a more general case) and the equilibrium free energy. It has been successfully applied to predict long range correlations [2], large deviations [3,4], fluctuation induced forces [5], dynamical phase transitions [6][7][8][9][10], their associated critical exponents [11,12] and many more [13,14]. It has been the aim of several studies to build on the ideas of the macroscopic fluctuation theory and to generalize its range of validity in both classical [15][16][17], and quantum systems [18,19].…”