Deterministic model of battery, uphill currents and non-equilibrium phase transitions

TL;DR

This paper models a deterministic, conservative system of particles in a loop with threshold-based bounce-back mechanisms, demonstrating non-equilibrium phase transitions and stationary currents akin to a battery in the infinite particle limit.

Contribution

It introduces a novel deterministic model with threshold-induced bounce-back, showing non-equilibrium phase transitions and stationary currents in a closed-loop particle system.

Findings

Non-equilibrium phase transitions occur with proper parameter tuning.

A stationary current emerges in the infinite particle limit.

The model exhibits battery-like behavior despite being deterministic and time-reversal invariant.

Abstract

We consider point particles in a table made of two circular cavities connected by two rectangular channels, forming a closed loop under periodic boundary conditions. In the first channel, a bounce--back mechanism acts when the number of particles flowing in one direction exceeds a given threshold $T$. In that case, the particles invert their horizontal velocity, as if colliding with vertical walls. The second channel is divided in two halves parallel to the first, but located in the opposite sides of the cavities. In the second channel, motion is free. We show that, suitably tuning the sizes of cavities, of the channels and of $T$, non--equilibrium phase transitions take place in the $N\rightarrow \infty$ limit. This induces a stationary current in the circuit, thus modeling a kind of battery, although our model is deterministic, conservative, and time reversal invariant.