Dynamical large deviations for long-range interacting inhomogeneous systems without collective effects

TL;DR

This paper derives a large deviation principle for the long-term evolution of inhomogeneous long-range interacting systems, extending kinetic theory by quantifying the probabilities of fluctuations without collective effects.

Contribution

It introduces a large deviation framework for inhomogeneous long-range systems, generalizing the inhomogeneous Landau equation to include fluctuation probabilities.

Findings

Large deviation principle for empirical distribution functions.

Hamiltonian respects conservation laws and has a gradient structure.

Extension of kinetic theory to fluctuation regimes.

Abstract

We consider the long-term evolution of an inhomogeneous long-range interacting $N$-body system. Placing ourselves in the dynamically hot limit, i.e. neglecting collective effects, we derive a large deviation principle for the system's empirical angle-averaged distribution function. This result extends the classical ensemble-averaged kinetic theory given by the so-called inhomogeneous Landau equation, as it specifies the probability of typical and large dynamical fluctuations. We detail the main properties of the associated large deviation Hamiltonian, in particular how it complies with the system's conservation laws and possesses a gradient structure.