We explore the thermodynamics of stochastic heat engines in presence of stochastic resetting. The set-up comprises an engine whose working substance is a Brownian particle undergoing overdamped Langevin dynamics in a harmonic potential with a time-dependent stiffness, with the dynamics interrupted at random times with a resetting to a fixed location. The effect of resetting to the potential minimum is shown to enhance the efficiency of the engine, while the output work is shown to have a non-monotonic dependence on the rate of resetting. The resetting events are found to drive the system out of linear response regime even for small differences in the bath temperatures. Shifting the reset point from the potential minimum is observed to reduce the engine efficiency. The experimental set-up for the realization of such an engine is briefly discussed.
We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the resetting position are Gaussian distributed with width $σ$. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean fi…
We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a nonthermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in the case of a purely thermal bath, the distribution is double exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate, is investigated carefully. In addition, we study …
The model of binary aggregation with constant kernel is subjected to stochastic resetting: aggregates of any size explode into monomers at independent stochastic times. These resetting times are Poisson distributed, and the rate of the process is called the resetting rate. The master equation yields a Bernoulli-type equation in the generating function of the concentration of aggregates of any size, which can be solved exactly. This resetting prescription leads to a non-equilibrium steady state for the densities of aggregates, which is a function of the size of the aggregate, rescaled by a func…
We consider a random walker on a ring, subjected to resetting at Poisson-distributed times to the initial position (the walker takes the shortest path along the ring to the initial position at resetting times). In the case of a Brownian random walker the mean first-completion time of a turn is expressed in closed form as a function of the resetting rate. The value is shorter than in the ordinary process if the resetting rate is low enough. Moreover, the mean first-completion time of a turn can be minimised in the resetting rate. At large time the distribution of winding numbers does not reach …
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the possibility of modeling a wide variety of realistic systems but also leads to interesting novel phenomenology not present in reset-free cases. However, most models where stochastic resetting is studied address the case of a finite number of uncorrelated variables, commonly a single one, such as the position of non-interacting random walkers. Here we overcome this …
We study a non-interacting quantum particle, moving on a one-dimensional lattice, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial configuration, known as the quantum resetting problem. We show that such systems can be described by the time evolution under certain time-dependent non-Hermitian Hamiltonians. We construct two such Hamiltonians and compare the results with the exact dynamics. Using this effective non-Hermitian description we evaluate the timescale of the survival probability as well as…
We study the Stochastic Thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to an identical copy of itself, and resetting, by which some properties of the daughter cells (such as their size or age) are reset to new values following division. We derive the first and second laws of Stochastic Thermodynamics for this process, and identify separate contributions due to branching and resetting. We apply our framework to well-known models o…
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 p…
We consider one dimensional diffusive search strategies subjected to external potentials. The location of a single target is drawn from a given probability density function (PDF) $f_G(x)$ and is fixed for each stochastic realization of the process. We optimize the quality of the search strategy as measured by the mean first passage time (MFPT) to the position of the target. For a symmetric but otherwise arbitrary distribution $f_G(x)$ we find the optimal potential that minimizes the MFPT. The minimal MFPT is given by a nonstandard measure of the dispersion, which can be related to the cumulati…
We study the optimal performance of an endoreversible quantum dot heat engine, in which the heat transfer between the system and baths is mediated by qubits, operating under the conditions of a trade-off objective function known as maximum efficient power function defined by the product of power and efficiency of the engine. First, we numerically study the optimization of the efficient power function for the engine under consideration. Then, we obtain some analytic results by applying hightemperature limit and compare the performance of the engine at maximum efficient power functionto the engi…
Miniaturized heat engines constitutes a fascinating field of current research. They are being studied theoretically as well as experimentally, with experiments involving colloidal particles and harmonic traps and even bacterial baths acting like thermal baths. They are interesting to study because usual equilibrium thermodynamic notions can not be applied directly to these systems. These systems are micron sized or even smaller and they are subjected to laud thermal fluctuations. Thus one needs to study the behavior of such systems in terms of these fluctuations. Average thermodynamic quantiti…
We study how a quantum heat engine performs across the critical value of an external parameter, pertaining to the quantum phase transition. Considering a two-ion system subjected to a magnetic field, we show that the system performs in a quantum Otto cycle above a critical value of the magnetic field, while below such critical point, it does not operate in a heat cycle at all. Moreover, at the critical point, its interaction with an ancillary ion deteriorates the performance of the system as a heat engine. We further show that a strong interaction between the constituent ions of an ion-based s…
Quantum heat engines are subjected to quantum fluctuations related to their discrete energy spectra. Such fluctuations question the reliable operation of quantum engines in the microscopic realm. We here realize an endoreversible quantum Otto cycle in the large quasi-spin states of Cesium impurities immersed in an ultracold Rubidium bath. Endoreversible machines are internally reversible and irreversible losses only occur via thermal contact. We employ quantum control over both machine and bath to suppress internal dissipation and regulate the direction of heat transfer that occurs via inelast…
Effects of Magnetic Anisotropy on 3-Qubit Antiferromagnetic Thermal Machines
Pontificia Universidad Católica de Valparaíso（天主教瓦爾帕萊索大學）；Universidad Técnica Federico Santa María（費德里科·聖塔瑪麗亞理工大學）；Millennium Nucleus in NanoBioPhysics (NNBP)（納米生物物理千年核）；Universidad Mayor（馬約爾大學）；Ohio University（俄亥俄大學）
