Measurements of any property of a microscopic system are bound to show significant deviations from the average, due to thermal fluctuations. For time-integrated currents such as heat, work or entropy production in a steady state, it is in fact known that there will be long stretches of fluctuations both above as well as below the average, occurring equally likely at large times. In this paper we show that for any finite-time measurement in a non-equilibrium steady state - rather counter-intuitively - fluctuations below the average are more probable. This discrepancy is higher when the system is further away from equilibrium. For overdamped diffusive processes, there is even an optimal time when time-integrated current fluctuations mostly lie below the average. We demonstrate that these effects result from the non-monotonic skewness of current fluctuations and provide evidence that they are easily observable in experiments. We also discuss their extensions to discrete space Markov jump processes and implications to biological and synthetic microscopic engines.
Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to dynamics and thermodynamics of a transport setup. Specifically, several distinct bounds on these quantities are either analytically derived or numerically conjectured, which are applicable to: 1) noninteracting fermionic systems, 2) noninteracting bosonic systems, 3) thermally driven classical Markovian systems, 4) unicyclic Markovian networks. Finally, it is demo…
We utilize the concept of a measurement-induced entanglement transition to analyze the interplay and competition of processes that generate and destroy entanglement in a one-dimensional quantum spin chain evolving under a locally noisy and disordered Hamiltonian. We employ continuous measurements of variable strength to induce a transition from volume to area-law scaling of the steady-state entanglement entropy. While static background disorder systematically reduces the critical measurement strength, this critical value depends non-monotonically on the strength of non-static noise. According …
Thermodynamic Networks: Harnessing Non-Equilibrium Steady States for Computation
Polish Academy of Sciences（波兰科学院）；Jagiellonian University（雅盖隆大学）；University of Geneva（日内瓦大学）；Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB)（复杂系统与交叉物理研究所（西班牙国家研究委员会-巴利阿里群岛大学））；Universitat Autònoma de Barcelona（巴塞罗那自治大学）
On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems
本文讨论了在不同温度下与两个确定性恒温器接触的力学系统的瞬态和稳态涨落关系。该系统是一个修改的洛伦兹气体中的固定散射体与气体的粒子交换能量，和恒温器是由两个Nosé-胡佛恒温器应用在系统的边界模拟。瞬态波动关系，它只适用于一个精确的选择初始合奏，验证在任何时候，正如预期的那样。如果考虑不同的初始系综，则需要比局部平衡所需的介观尺度更长的时间。这表明，如在我们的系统中明确检查的，当[D.J.Searles，{\em et al.}，J. Stat. Phys.128，1337（2007）]中的方法，验证了稳态涨落关系的有效性。对于稳态波动的相空间收缩率$\zL$和耗散函数$\zW$，一个类似的松弛制度在较短的平均时间被发现。量$\zW$满足良好的精度波动关系的时间大于介观时间尺度;量$\zL$出现后开始单调收敛。这与$\zW$和$\zL$相差一个总时间导数，以及$\zL$的概率分布函数的尾部是高斯分布的事实是一致的。
Local imperfect feedback control in non-equilibrium biophysical systems enabled by thermodynamic constraints
The University of Chicago（芝加哥大学）；The Chicago Center for Theoretical Chemistry（芝加哥理论化学中心）；Department of Chemistry, The University of Chicago（芝加哥大学化学系）；The James Franck Institute（詹姆斯·弗兰克研究所）
We consider an active Brownian particle in a $d$-dimensional harmonic trap, in the presence of translational diffusion. While the Fokker-Planck equation can not in general be solved to obtain a closed form solution of the joint distribution of positions and orientations, as we show, it can be utilized to evaluate the exact time dependence of all moments, using a Laplace transform approach. We present explicit calculation of several such moments at arbitrary times and their evolution to the steady state. In particular we compute the kurtosis of the displacement, a quantity which clearly shows t…
