论文标题
重置过程的熵产生
Entropy production of resetting processes
论文作者
论文摘要
近年来，在理论上还是在实验中，都广泛研究了随机重新启动到其初始状态的随机系统。但是，由于热噪声或其他局限性，通常不可能重置为固定状态。结果，重置事件后的系统配置是随机的。在这里，我们考虑了在限制潜在$ V（x）$中的过度引导的布朗粒子的重置协议。我们假设粒子的位置以恒定速率重置为随机位置$ x $，是从分布$ p_r（x）$中绘制的。为了研究重置的热力学成本，我们研究了随机熵产生$ s _ {\ rm总计} $。我们为任何$ v（x）$的平均熵产生提供了一般表达，以及$ v（x）= 0 $的熵生产的完整分布$ p（s _ {\ rm total} | t）$。在后期，我们表明此分布假定大泄漏表$ p（s _ {\ rm tatre} | t）\ sim \ exp \ left [-t^{2α-1} ϕ \ left（\ left（s _ {\ rm tatre} - 总} \ rangle \ right）/t^α\ right）\ right] $，$ 1/2 <α\ leq 1 $。我们计算速率函数$ ϕ（z）$和指数和高斯重置分布的指数$α$。在后一种情况下，我们发现异常指数$α= 2/3 $，并表明$ ϕ（z）$的一阶奇点，临界值为$ z $，对应于真实空间的冷凝转换。
Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and in experiments. Oftentimes, however, resetting to a fixed state is impossible due to thermal noise or other limitations. As a result, the system configuration after a resetting event is random. Here, we consider such a resetting protocol for an overdamped Brownian particle in a confining potential $V(x)$. We assume that the position of the particle is reset at a constant rate to a random location $x$, drawn from a distribution $p_R(x)$. To investigate the thermodynamic cost of resetting, we study the stochastic entropy production $S_{\rm Total}$. We derive a general expression for the average entropy production for any $V(x)$, and the full distribution $P(S_{\rm Total}|t)$ of the entropy production for $V(x)=0$. At late times, we show that this distribution assumes the large-deviation form $P(S_{\rm Total}|t)\sim \exp\left[-t^{2α-1}ϕ\left(\left(S_{\rm Total}-\langle S_{\rm Total}\rangle\right)/t^α\right)\right]$, with $1/2<α\leq 1$. We compute the rate function $ϕ(z)$ and the exponent $α$ for exponential and Gaussian resetting distributions. In the latter case, we find the anomalous exponent $α=2/3$ and show that $ϕ(z)$ has a first-order singularity at a critical value of $z$, corresponding to a real-space condensation transition.
