Dynamic phase transition theory

TL;DR

This paper introduces a statistical approach using ensemble theory in trajectory space to identify dynamic phase transitions, which are not well-described by traditional thermodynamics, by analyzing zeros of the dynamic partition function.

Contribution

It proposes a novel framework for understanding dynamic phase transitions through trajectory space ensemble theory, linking zeros of the dynamic partition function to phase boundaries.

Findings

Zeros of the dynamic partition function mark phase transitions in space-time.

Dynamic field acts as a potential controlling the phase transition.

Unified picture of phase and phase transition is suggested.

Abstract

Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we present a statistical approach to address this problem.Rather than spatial particle-particle interaction which dominates thermodynamics, the temporal correlation of events dominates the dynamics. The zeros of dynamic partition function mark phase transitions in the space-time, i.e. dynamic phase transition (DPT), as Yang and Lee formulate traditional phase transitions, and hence determine dynamic phases on both sides of the zeros. Analogous to the role of temperature (pressure) as thermal (mechanical) potential, we interpret the controlling variable of DPT, i.e. dynamic field, as the dynamical potential. These findings offer possibility towards a unified picture of phase and phase transition.