# Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model

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## Abstract

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## 1. Introduction

## 2. Model and Methods

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Local Density Equation

#### Appendix A.2. Local Correlation Equation

#### Appendix A.3. Bulk-Adapted Boundary Conditions

## References

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**Figure 1.**Contour plot of the bulk current as a function of repulsion V and density $\rho $. Maxima with respect to $\rho $ are shown with full black lines. The vertical dashed line corresponds to $V=2{V}_{*}$.

**Figure 2.**Non-equilibrium stationary state (NESS) phase diagram of the 1D Katz–Lebowitz–Spohn (KLS) model with $V=2{V}_{*}$. Solid (respectively dashed) thick lines denote discontinuous (resp. continuous) phase transitions. Solid thin lines are lines at constant ${\rho}_{R}=0.45,\phantom{\rule{3.33333pt}{0ex}}0.75$ and 0.98 in the high-density (HD) phases, where we perform our dynamical analysis.

**Figure 3.**Relaxation rate ${\lambda}_{1}$ as a function of the left reservoir density ${\rho}_{L}$, for $V=2{V}_{*}$ and ${\rho}_{R}=0.75$, in the pair approximation (PA) (black lines, $N=50,100,200,400$ from top to bottom), domain wall theory (DWT) (dashed red line), modified DWT (mDWT) (solid red line) and extrapolation of finite size results (grey dots, see text for details).

**Figure 6.**Same as Figure 2, with dynamical transition lines predicted by the PA (blue lines) and the mDWT (red lines). See text for the distinction between solid and dashed red lines.

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**MDPI and ACS Style**

Pelizzola, A.; Pretti, M.; Puccioni, F. Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model. *Entropy* **2019**, *21*, 1028.
https://doi.org/10.3390/e21111028

**AMA Style**

Pelizzola A, Pretti M, Puccioni F. Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model. *Entropy*. 2019; 21(11):1028.
https://doi.org/10.3390/e21111028

**Chicago/Turabian Style**

Pelizzola, Alessandro, Marco Pretti, and Francesco Puccioni. 2019. "Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model" *Entropy* 21, no. 11: 1028.
https://doi.org/10.3390/e21111028