Landau-like expansion for phase transitions in stochastic resetting

Abstract

We develop a Landau-like theory to characterize phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two states or phases is characterized by the behavioral change in the order parameter of the system namely the optimal restart rate which can undergo a first-or second-order transition depending on the details of the system. Nonetheless, there is no generic understanding of how the optimal restart rate behaves close to the transition with respect to the system parameters and what precisely characterizes the nature of the transition. We build a comprehensive theory to investigate both the transitions which, we show, can be understood by analyzing the first passage time moments. Our approach predicts the emergence of first-and second-order transition lines between the two phases that merge at a tricritical point. Power of our formulation is demonstrated on two canonical paradigm setup, namely, the Michaelis-Menten chemical reaction and diffusion under restart.

Invariants of motion with stochastic resetting and space-time coupled returns

“…Stochastic motion with stochastic resetting is of considerable interest due to its broad applicability in statistical [1][2][3][4][5][6][7], chemical [8][9][10][11][12], and biological physics [13,14]; and due to its importance in computer science [15,16], computational physics [17,18], population dynamics [19][20][21], queuing theory [22][23][24] and the theory of search and first-passage [25][26][27]. Particularly, in statistical physics, such motion has become a focal point of recent studies owing to the rich non-equilibrium [2][3][4][5][6][28][29][30] and first-passage [31][32][33][34][35][36] phenomena it displays.…”

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

“…FIG.5: The same as in Fig.2, but for reset HDPs, computed for the scaling exponents of D(x) ∼ |x| γ being γ = 1 (panel (a)) and γ = −2 (panel (b)), corresponding to superand subdiffusive HDPs, respectively. The theoretical shorttime asymptotes(37) and(46) and the NESS-related longtime MSD and mean TAMSD plateaus given by expressions(40) and(44), respectively, are the dashed black lines. The magnitude of the diffusivity (17) is fixed in simulations to D0 = 1.…”

Searching for clusters of targets under stochastic resetting

“…We note that a related problem of diffusion with resetting on a one-dimensional domain with absorbing boundaries has been considered in [23,31] where the statistics of the time to be absorbed by either boundary were considered.…”