Universal splitting of phase transitions and performance optimization in driven collective systems

TL;DR

This paper demonstrates that non-equilibrium phase transition splitting persists across various coupling protocols and that optimized power and efficiency are achieved at intermediate switching rates in driven collective systems.

Contribution

It extends the understanding of phase transition splitting to finite-time coupling protocols and shows improved performance in heat engines with stochastic and deterministic switching.

Findings

Phase transition splitting is robust across different coupling schemes.

Intermediate switching rates optimize power and efficiency.

Efficiency approaches an ideal limit depending only on reservoir temperatures.

Abstract

Spontaneous symmetry breaking is a hallmark of equilibrium systems, typically characterized by a single critical point separating ordered and disordered phases. Recently, a novel class of non-equilibrium phase transitions was uncovered [Phys. Rev. Res. {\bf 7}, L032049 (2025)], showing that the combined effects of simultaneous contact with thermal baths at different temperatures and external driving forces can split the conventional order-disorder transition into two distinct critical points, determined by which ordered state initially dominates. We show the robustness of this phenomenon by extending a minimal interacting-spin model from the idealized case of simultaneous bath coupling to a finite-time coupling protocol. In particular, we introduce two protocols in which the system interacts with a single bath at a time: a stochastic protocol, where the system randomly switches between the baths at different temperatures, and a deterministic protocol where the coupling alternates periodically. Our analysis reveals two key results: (i) the splitting of phase transitions persists across all coupling schemes -- simultaneous, stochastic, and deterministic -- and (ii) different optimizations of power and efficiency in a collectively operating heat engine reveal that both the stochastic and deterministic protocols exhibit superior global performance at intermediate switching rates and periods when compared to simultaneous coupling. The global trade-off between power and efficiency is described by an expression solely depending on the temperatures of thermal reservoirs as the efficiency approaches to the ideal limit.