Second Law of Thermodynamics at Stopping Times

Thermodynamic cost for precision of general counting observables

We analytically derive universal bounds that describe the tradeoff between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the waiting times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting-time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.

Gambling demon and stopping-time fluctuation relation of a Brownian particle under a time-dependent trapping potential

A gambling demon is an external agent that can terminate a time-dependent driving protocol when a certain observable of the system exceeds a prescribed threshold. The gambling demon is examined in detail both theoretically and experimentally in a Brownian particle system under a compressing potential trap. Insight for choosing an appropriate work threshold for stopping is discussed. The energetics and the distributions of the stopping positions and stopping times are measured in simulations to gain further understanding of the process. Furthermore, the nonstationary and far-from-equilibrium stochastic process in the action of the gambling demon allows us to examine in detail some fundamental issues in stochastic thermodynamics, such as irreversibility and stopping-time fluctuation relation. Paradoxical violation of the stopping-time fluctuation relation can be reconciled in terms of the entropy production associated with fast hidden internal degrees of freedom. All the simulation or theoretical results are confirmed experimentally.

Fluctuation theorems and thermodynamic inequalities for nonequilibrium processes stopped at stochastic times

We investigate the thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of stopping-time fluctuation theorems. We derive second-law-like thermodynamic inequalities for the mean thermodynamic functional at stochastic stopping times, the bounds of which are even stronger than the thermodynamic inequalities resulting from the traditional fluctuation theorems when the stopping time is reduced to a deterministic one. Numerical verification is carried out for three well-known thermodynamic functionals, namely, entropy production, free energy dissipation, and dissipative work. These universal equalities and inequalities are valid for arbitrary stopping strategies, and thus provide a comprehensive framework with insights into the fundamental principles governing nonequilibrium systems.

Verification of Information Thermodynamics in a Trapped Ion System

Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.

Development and Experimental Study of Smart Solar Assisted Yogurt Processing Unit for Decentralized Dairy Value Chain

Yogurt production at the farm level is important for adding value to milk. In this study, a solar-assisted yogurt processing unit capable of performing the three processes of heating, fermentation, and cooling in a single unit was developed. It consisted of a circular chamber surrounded by a coil for heating by a solar vacuum tube collector and a pillow plate for cooling by a solar PV-powered chiller unit. Experiments were performed using 50, 40 and 30 L of raw milk under a constant water circulation rate of 50 L per minute for heating followed by a cooling process under 36, 18 and 6 rpm of stirrer speeds. The heat absorption rates of the milk were 5.48–0.31, 4.75–0.16 and 4.14–0.24 kW, and the heat removal rates from water ranged from 6.28–0.49, 5.58–0.49 and 4.88–0.69 kW for 50, 40 and 30 L of milk volume, respectively. The overall heat transfer efficiency was above 80% during the heating process. A stirring speed of 18 rpm was found to be optimal in terms of cooling speed and consistency of the yogurt. The total energy consumed was calculated to be 6.732, 5.559 and 4.207 kWh for a 50, 40 and 30 L batch capacity, respectively. The study offers a sustainable energy solution for the decentralized processing of raw milk, particularly in remote areas of the developing countries where access to electricity is limited.

Martingale-induced local invariance in progressive quenching

Progressive quenching (PQ) is a stochastic process during which one fixes, one after another, the degrees of freedom of a globally coupled Ising spin system while letting it thermalize through a heat bath. It has previously been shown that during PQ, the mean equilibrium spin value follows a martingale process and this process can characterize the memory of the system. In the present study, we find that the aforementioned martingale implies a local invariance of the path weight for the total quenched magnetization, the Markovian process whose increment is the spin that is fixed last. Consequently, PQ lets the probability distribution for the total quenched magnetization evolve while keeping the Boltzmann-like factor, or a canonical structure, under constraint, which consists of a path-independent potential and a path-counting entropy. Moreover, when the PQ starts from full equilibrium, the probability distribution at each stage of PQ is found to be the limit distribution of what we call recycled quenching, the process in which a randomly chosen quenched spin is unquenched after a single step of PQ. The local invariance is directly derived from the martingale property, and not from other known theorems on martingale processes.

Thermodynamic uncertainty relation for quantum first-passage processes

We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains. We consider first passage processes that stop after a fixed number of jump events, which contrasts with typical quantum Markov chains which end at a fixed time. We obtain bounds for the observables of the first passage processes in quantum Markov chains by the Loschmidt echo, which quantifies the extent of irreversibility in quantum many-body systems. Considering a particular case, we show that the lower bound corresponds to the quantum Fisher information, which plays a fundamental role in uncertainty relations in quantum systems. Moreover, considering classical dynamics, our bound reduces to a thermodynamic uncertainty relation for classical first passage processes.

Experimental Verification of Dissipation-Time Uncertainty Relation

Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.

Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines

We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent thresholds that these quantities do not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results entail an extension of martingale theory for entropy production, for which we derive universal inequalities involving its maximum and minimum statistics that are valid for generic Markovian dynamics in nonequilibrium stationary states. We test our main results with numerical simulations of a stochastic photoelectric device.

Thermodynamics of Gambling Demons

We introduce and realize demons that follow a customary gambling strategy to stop a nonequilibrium process at stochastic times. We derive second-law-like inequalities for the average work done in the presence of gambling, and universal stopping-time fluctuation relations for classical and quantum nonstationary stochastic processes. We test experimentally our results in a single-electron box, where an electrostatic potential drives the dynamics of individual electrons tunneling into a metallic island. We also discuss the role of coherence in gambling demons measuring quantum jump trajectories.

Dissipation-Time Uncertainty Relation

We show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff ⟨S[over ˙]_{e}⟩T≥k_{B} between the entropy flow ⟨S[over ˙]_{e}⟩ into the reservoirs and the mean time T to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.