Discontinuous phase transition switching induced by a power-law function between dynamical parameters in coupled...

Area of Science:

• Physics
• Complex Systems
• Nonlinear Dynamics

Background:

• Oscillators in biological and physical systems exhibit heterogeneous and correlated intrinsic properties.
• These characteristics are empirically validated and are subjects of theoretical investigation.

Purpose of the Study:

• To propose a power-law function between dynamical parameters of coupled oscillators.
• To demonstrate this function's ability to control discontinuous phase transition switching.
• To reveal a novel pathway for generating first-order phase transitions via dynamical terms.

Main Methods:

• Introduction of a generalized power-law function within the dynamical term of coupled oscillators.
• Analysis of the function's impact on phase transition dynamics.
• Comparison with existing methods focusing on coupling terms.

Main Results:

• The proposed power-law function controls discontinuous phase transition switching.
• This generalized function offers an alternative route to first-order phase transitions.
• Empirical support for the power-law relationship in natural phenomena like volcanic tremors and ion channels.

Conclusions:

• The study expands the conditions required for first-order phase transitions.
• It deepens the understanding of how correlations in intrinsic parameters influence phase transitions.
• Provides an explanation for the switch from continuous to discontinuous phase transitions at critical values.