Entropy production of resetting processes

Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and experiments. Oftentimes, however, resetting a fixed is impossible due thermal noise or other limitations. As result, the system configuration after event random. Here, we consider such protocol for an overdamped Brownian particle confining potential $V(x)$. We assume position of reset at constant rate location $x$, drawn from distribution ${p}_{R}(x)$. To investigate thermodynamic cost resetting, study stochastic entropy production ${S}_{\mathrm{Total}}$. derive general expression average any $V(x)$, full $P({S}_{\mathrm{Total}}|t)$ $V(x)=0$. At late times, show this assumes large-deviation form $P({S}_{\mathrm{Total}}|t)\ensuremath{\sim}exp{\ensuremath{-}{t}^{2\ensuremath{\alpha}\ensuremath{-}1}\ensuremath{\phi}[({S}_{\mathrm{Total}}\ensuremath{-}\ensuremath{\langle}{S}_{\mathrm{Total}}\ensuremath{\rangle})/{t}^{\ensuremath{\alpha}}]}$, with $1/2<\ensuremath{\alpha}\ensuremath{\le}1$. compute function $\ensuremath{\phi}(z)$ exponent $\ensuremath{\alpha}$ exponential Gaussian distributions In latter case, find anomalous $\ensuremath{\alpha}=2/3$ has first-order singularity critical value $z$, corresponding real-space condensation transition.