In this paper we consider a threshold surface absorption mechanism for a particle diffusing in a domain containing a single target $\calU $. The target boundary $\partial \calU$ is taken to be a reactive surface that modifies an internal state $Z_t$ of the particle when in contact with the surface at time $t$, with $Z_0=h$. The state $Z_t$ is taken to be a monotonically decreasing function of the so-called boundary local time, and absorption occurs as soon as $Z_t$ reaches zero. (The boundary local time is a Brownian functional that determines the amount of time that the particle spends in a neighborhood of $\partial \calU$.) We first show how to analyze threshold surface absorption in terms of the joint probability density or generalized propagator $P_0(\x,\ell,t|\x_0)$ for the pair $(\X_t,\ell_t)$ in the case of a perfectly reflecting surface, where $\X_t$ and $\ell_t$ denote the particle position and local time at time $t$, respectively, and $\x_0$ is the initial position. We then introduce a generalized stochastic resetting protocol in which both the position $\X_t$ and the internal state $Z_t$ are reset to their initial values, $\X_t\rightarrow \x_0$ and $Z_t\rightarrow h$, at a Poisson rate $r$. The latter is mathematically equivalent to resetting the boundary local time, $\ell_t\rightarrow 0$. Since resetting is governed by a renewal process, the survival probability with resetting can be expressed in terms of the survival probability without resetting, which means that the statistics of absorption can be determined by calculating the Laplace transform of $P_0(\x,\ell,t|\x_0)$ with respect to $t$. We contrast this with the case where only particle position is reset, which is not governed by a renewal process. We illustrate the theory using the simple examples of diffusion on the half-line and a spherical target in a spherical domain.
Non-equilibrium dynamics of drift-diffusion process under threshold resetting
The Institute of Mathematical Sciences（马哈拉施特拉数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université de Paris-Sud（巴黎南大学理论与统计物理实验室）
Stochastic synthesis-degradation processes: first-passage properties and connections with resetting
Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）
The Institute of Mathematical Sciences（数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS, Univ. Paris-Sud, Universite Paris-Saclay（理论与统计物理实验室（LPTMS），法国国家科学研究中心，巴黎第十一大学，巴黎萨克雷大学）
Optimal threshold resetting in collective diffusive search
The Institute of Mathematical Sciences（马修研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）；School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université de Paris-Sud, Université Paris-Saclay（巴黎第十一大学/萨克雷大学理论与统计物理实验室）
University of Chicago（芝加哥大学）；LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay（巴黎第十一大学、法国国家科学研究中心理论物理实验室）；Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589（索邦大学、CNRS高能理论物理联合研究单位）
