We provide a strategy for the exact inference of the average as well as the fluctuations of the entropy production in non-equilibrium systems in the steady state, from the measurements of arbitrary current fluctuations. Our results are built upon the finite-time generalization of the thermodynamic uncertainty relation, and require only very short time series data from experiments. We illustrate our results with exact and numerical solutions for two colloidal heat engines. arXiv:1910.00476v2 [cond-mat.stat-mech]
We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate r whereas its velocity evolves irrespective of the position of the particle and stochastic resetting mechanism. The nonequilibrium steady state of the position distribution is studied for this model system. Further, we study the distribution of the position of the particle in the finite time and the approach to the nonequilibrium steady state distribution with time. Numerical simulations are done to verify the analytical results.
We consider the paradigm of an overdamped Brownian particle in a potential well, which is modulated through an external protocol, in the presence of stochastic resetting. Thus, in addition to the short range diffusive motion, the particle also experiences intermittent long jumps which reset the particle back at a preferred location. Due to the modulation of the trap, work is done on the system and we investigate the statistical properties of the work fluctuations. We find that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event. When observed for a finite time, we show that the system does not generically obey the Jarzynski equality which connects the finite time work fluctuations to the difference in free energy, albeit a restricted set of protocols which we identify herein. In stark contrast, the Jarzynski equality is always fulfilled when the protocols continue to evolve without being reset. We present a set of exactly solvable models, demonstrate the validation of our theory and carry out numerical simulations to illustrate these findings.Introduction.-Stochastic thermodynamics is a cornerstone in non-equilibrium statistical physics [1][2][3][4][5]. Microscopic systems satisfy stochastic laws of motion governed by force fields and thermal fluctuations which arise due to the surrounding. The subject then teaches us that thermodynamic observables such as work, heat, entropy production etc. measured along the stochastic trajectories taken from ensembles of such dynamics will fluctuate too. Understanding the distribution and the statistical properties of these fluctuations is of great interest since they hold a treasure trove of information about microscopic systems and how they respond to external perturbation. Indeed there has been a myriad of studies to understand e.g., non-equilibrium dynamics of biopolymers [6,7], colloidal particles [8][9][10][11][12][13], efficiency of molecular bio-motors [14,15] and microscopic engines [16], heat conduction [17,18], electronic transport in quantum systems [19], trapped-ion systems [20] and many more [21]. Despite there exists a long catalogue of such diverse small systems with no apparent similarity, it is quite remarkable to find universal relations which are obeyed regardless. One of the most celebrated ones is perhaps the Jarzynski equality (JE) that relates the non-equilibrium fluctuations of the work to the equilibrium free energy difference [22][23][24]. Universalities of such kind have always been considered as a holy grail in physical sciences and in this paper we seek out for thermodynamic invariant principles in stochastic resetting systems [25].Dynamics with stochastic reset has drawn a lot of attention recently because of its rich non-equilibrium properties [25][26][27][28][29][30][31][32][33][34][35][36][37] and its broad applicability in first passage processes [38][39][40][41][42][43][44][45][46][47]. Nevertheless, thermodyna...
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