# Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

## TL;DR

This paper investigates how finite-size and finite-time effects influence large deviation functions in a simple particle hopping model, revealing symmetry-breaking dynamical phase transitions and critical phenomena analogous to extended systems.

## Contribution

It introduces a minimal model to study dynamical phase transitions, providing exact characterizations and finite-size scaling analysis, which are difficult to access in extended systems.

## Key findings

- Identification of symmetry-breaking dynamical phase transitions in a zero-dimensional model.
- Quantification of finite-size and finite-time scaling exponents.
- Discovery of critical slowing down near symmetry-breaking transitions.

## Abstract

We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity large deviation functions of the models can exhibit symmetry-breaking dynamical phase transitions. We characterize exactly the critical properties of these transitions, showing them to be direct analogues of previously studied phase transitions in extended systems. The simplicity of the model allows us to study features of dynamical phase transitions which are not readily accessible for extended systems. In particular, we quantify finite-size and finite-time scaling exponents using both numerical and theoretical arguments. Importantly, we identify an analogue of critical slowing near symmetry breaking transitions and suggest how this can be used in the numerical studies of large deviations. All of our results are also expected to hold for extended systems.