Landau theory of restart transitions

Abstract

We develop a Landau like theory to characterize the phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two phases is characterized by the behavioral change in the order parameter of the system namely the optimal restart rate. Like in the original theory of Landau, the optimal restart rate can undergo a first or second order transition depending on the details of the system. Nonetheless, there exists no unified framework which can capture the onset of such novel phenomena. We unravel this in a comprehensive manner and show how the transition can be understood by analyzing the first passage time moments. Power of our approach is demonstrated in two canonical paradigm setup namely the Michaelis Menten chemical reaction and diffusion under restart.

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• Stochastic Resetting and Applications
• Experimental realization of diffusion with stochastic resetting
• Stochastic resetting: A (very) brief review
• Search with home returns provides advantage under high uncertainty
• The inspection paradox in stochastic resetting
• Work fluctuations and Jarzynski equality in stochastic resetting
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• Invariants of motion with stochastic resetting and space-time coupled returns
• Thermodynamic uncertainty relation for systems with unidirectional transitions
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• Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling
• First passage time in space-dependent stochastic resetting
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