Single Heat Bath Research Articles

Active Brownian information engine: Self-propulsion induced colossal performance.

The information engine is a feedback mechanism that extorts work from a single heat bath using the mutual information earned during the measurement. We consider an overdamped active Ornstein-Uhlenbeck particle trapped in a 1D harmonic oscillator. The particle experiences fluctuations from an inherent thermal bath with a diffusion coefficient (D) and an active reservoir, with characteristic correlation time (τa) and strength (Da). We design a feedback-driven active Brownian information engine (ABIE) and analyze its best performance criteria. The optimal functioning criteria, the information gained during measurement, and the excess output work are reliant on the dispersion of the steady-state distribution of the particle's position. The extent of enhanced performance of such ABIE depends on the relative values of two underlying time scales of the process, namely, thermal relaxation time (τr) and the characteristic correlation time (τa). In the limit of τa/τr → 0, one can achieve the upper bound on colossal work extraction as ∼0.202γ(D+Da) (γ is the friction coefficient). The excess amount of extracted work reduces and converges to its passive counterpart (∼0.202γD) in the limit of τa/τr → high. Interestingly, when τa/τr = 1, half the upper bound of excess work is achieved irrespective of the strength of either reservoirs, thermal or active. Finally, we look into the average displacement of active Brownian particles in each feedback cycle, which surpasses its thermal analog due to the broader marginal probability distribution.

Resource engines

In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based predominantly on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two–stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.

Necessity of feedback control for the quantum Maxwell demon in a finite-time steady feedback cycle

We revisit quantum Maxwell demon in thermodynamic feedback cycle in the steady-state regime. We derive a generalized version of the Clausius inequality for a finite-time steady feedback cycle with a single heat bath. It is shown to be tighter than previously known ones, and allows us to clarify that feedback control is necessary to violate the standard Clausius inequality.

Experimental investigation of a quantum heat engine powered by generalized measurements

Generalized measurements may allow the control of its back-action on the quantum system by interpolating from a very weak to strong projective action. Such a measurement can fuel a quantum heat engine or extract work depending on the system-meter interaction. Here, we performed a proof-of-concept experiment using nuclear magnetic resonance techniques to investigate a spin quantum heat engine driven by non-selective generalized (weak) measurements without feedback control. Our prototype of a quantum thermal device operates with a measurement protocol and a single heat bath. The protocol is composed of two non-selective measurement channels with variable measurement strengths, one dedicated to fueling the device (analogous to a hot heat source) and the other committed to work extraction. The experimental results highlight that this kind of quantum thermal device can reach unit efficiency with maximum extracted power by fine-tuning of the measurement strengths.

Thermodynamic Discrimination between Energy Sources for Chemical Reactions

Summary Chemical transformations traverse large energy differences, yet the comparison of energy sources to drive a reaction is often done on a case-by-case basis; there is no fundamentally driven, universal framework with which to analyze and compare driving forces for chemical reactions. In this work, we present a reaction-independent expression for the equilibrium constant as a function of temperature, pressure, and voltage. With a specific set of axes, all reactions are represented by a single ( x , y ) point, and a quantitative divide between electrochemically and thermochemically driven reactions is visually evident. Additionally, we show that our expression has a strong physical basis in work and energy fluxes to the system, although specific data about operating conditions are necessary to provide a quantitative energy analysis. Overall, this universal equation and facile visualization of chemical reactions provides a consistent thermodynamic framework for comparing electrochemical versus thermochemical energy sources without knowledge of detailed process parameters.

Irreversibility, heat and information flows induced by non-reciprocal interactions

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled degrees of freedom renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. We demonstrate that non-reciprocal linear interactions can be used to engineer non-monotonic memory, which is typical for, e.g., time-delayed feedback control, and is automatically accompanied with a nonzero information flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous ‘Maxwell demon’. We also show that for appropriate parameter settings, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the fluctuating trajectories without global particle transport.

Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force.

The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system-bath composite. We make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the Hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom. In doing so, we refute a key criticism expressed in the works by P. Talkner and P. Hänggi [Phys. Rev. E 94, 022143 (2016)10.1103/PhysRevE.94.022143 and arXiv:1911.11660]. We also discuss the remaining part of the criticism.

Double quantum-dot engine fueled by entanglement between electron spins

The laws of thermodynamics allow work extraction from a single heat bath provided that the entropy decrease of the bath is compensated for by another part of the system. We propose a thermodynamic quantum engine that exploits this principle and consists of two electrons on a double quantum dot (QD). The engine is fueled by providing it with singlet spin states, where the electron spins on different QDs are maximally entangled, and its operation involves only changing the tunnel coupling between the QDs. Work can be extracted since the entropy of an entangled singlet is lower than that of a thermal (mixed) state, although they look identical when measuring on a single QD. We show that the engine is an optimal thermodynamic engine in the long-time limit. In addition, we include a microscopic description of the bath and analyze the engine's finite-time performance using experimentally relevant parameters.

Stochastic thermodynamics with arbitrary interventions.

We extend the theory of stochastic thermodynamics in three directions: (i) instead of a continuously monitored system we consider measurements only at an arbitrary set of discrete times, (ii) we allow for imperfect measurements and incomplete information in the description, and (iii) we treat arbitrary manipulations (e.g., feedback control operations) which are allowed to depend on the entire measurement record. For this purpose we define for a driven system in contact with a single heat bath the four key thermodynamic quantities-internal energy, heat, work, and entropy-along a single "trajectory" for a causal model. The first law at the trajectory level and the second law on average is verified. We highlight the special case of Bayesian or "bare" measurements (incomplete information, but no average disturbance) which allows us to compare our theory with the literature and to derive a general inequality for the estimated free energy difference in Jarzynski-type experiments. An analysis of a recent Maxwell demon experiment using real-time feedback control is also given. As a mathematical tool, we prove a classical version of Stinespring's dilation theorem, which might be of independent interest.

Physical limitations of work extraction from temporal correlations.

Recently proposed information-exploiting systems extract work from a single heat bath by using temporal correlations on an input tape. We study how enforcing time-continuous dynamics, which is necessary to ensure that the device is physically realizable, constrains possible designs and drastically diminishes efficiency. We show that these problems can be circumvented by means of applying an external, time-varying protocol, which turns the device from a "passive," free-running machine into an "actively" driven one.

Non-Markovianity and negative entropy production rates.

Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.

Optimal tuning of a Brownian information engine operating in a nonequilibrium steady state

A Brownian information engine can induce directed motion of a Brownian particle in a single heat bath at constant temperature by extracting work from the information about the microscopic state of the particle, and serves as a model for artificial and biological submicron scale engines. Much of the experimental studies to date are limited to the realization of an information engine where the initial state of the system is in thermal equilibrium; however, most of the biological and artificial motors operate far from equilibrium. Here, we realize a cyclic information engine operating in a nonequilibrium steady state consisting of a Brownian particle in an optical trap and investigate the optimal operating conditions for maximum work, power, and efficiency. The performance of our information engine depends on the cycle period $\ensuremath{\tau}$ and the distance ${x}_{f}$ that the trap center is shifted with respect to the reference distance ${x}_{m}$. We found that the extracted work increases with increasing $\ensuremath{\tau}$ and is maximum when $\ensuremath{\tau}$ reaches infinity and ${x}_{f}=2{x}_{m}$, while the extracted power is maximum at finite $\ensuremath{\tau}$ for ${x}_{f}\ensuremath{\ge}{x}_{m}$ and when $\ensuremath{\tau}$ approaches zero for ${x}_{f}l{x}_{m}$. By measuring the steady-state information, we have also measured the efficiency at maximum power.

Measurement-driven single temperature engine

A four stroke quantum engine which alternately interacts with a measurement apparatus and a single heat bath is discussed in detail with respect to the average work and heat as well as to the fluctuations of work and heat. The efficiency and the reliability of such an engine with a harmonic oscillator as working substance are analyzed under different conditions such as different speeds of the work strokes, different temperatures of the heat bath and various strengths of the energy supplying measurement. For imperfect thermalization strokes of finite duration also the power of the engine is analyzed. A comparison with a two-temperature Otto engine is provided in the particular case of adiabatic work and ideal thermalization strokes.

An experimentally-achieved information-driven Brownian motor shows maximum power at the relaxation time

We present an experimental realization of an information-driven Brownian motor by periodically cooling a Brownian particle trapped in a harmonic potential connected to a single heat bath, where cooling is carried out by the information process consisting of measurement and feedback control. We show that the random motion of the particle is rectified by symmetry-broken feedback cooling where the particle is cooled only when it resides on the specific side of the potential center at the instant of measurement. Studying how the motor thermodynamics depends on cycle period τ relative to the relaxation time τB of the Brownian particle, we find that the ratcheting of thermal noise produces the maximum work extraction when τ ≥ 5τB, while the extracted power is maximum near τ = τB, implying the optimal operating time for the ratcheting process. In addition, we find that the average transport velocity is monotonically decreased as τ increases and present the upper bound for the velocity.

Partial entropy production in heat transport

We consider a system of two Brownian particles (say A and B), coupled to each other via harmonic potential of stiffness constant k. Particle-A is connected to two heat baths of constant temperatures T1 and T2, and particle-B is connected to a single heat bath of a constant temperature T3. In the steady state, the total entropy production for both particles obeys the fluctuation theorem. We compute the total entropy production due to particle-A in the coupled system (partial and apparent entropy production) in the steady state for a time segment τ. When both particles are weakly interacting with each other, the fluctuation theorem for partial and apparent entropy production is studied. We find a significant deviation from the fluctuation theorem. The analytical results are also verified using numerical simulations. Furthermore, we investigate the effect of hidden fast degrees of freedom on the steady state fluctuation theorem for a system of a single Brownian particle coupled to two heat baths of distinct temperatures and dissipation constants, and coupled to a third heat bath of vanishing temperature and dissipation constant.

Transient exchange fluctuation theorems for heat using a Hamiltonian framework: Classical and quantum regimes.

We investigate the statistics of heat exchange between a finite system coupled to reservoir(s). We have obtained analytical results for heat fluctuation theorems in the transient regime considering the Hamiltonian dynamics of the composite system consisting of the system of interest and the heat bath(s). The system of interest is driven by an external protocol. We first derive it in the context of a single heat bath. The result is in exact agreement with known result. We then generalize the treatment to two heat baths. We further extend the study to quantum systems and show that relations similar to the classical case hold in the quantum regime. For our study we invoke von Neumann two-point projective measurement in quantum mechanics in the transient regime. The study of quantum systems follows the same lines of argument as that of the classical system, and as a result the treatment used in the latter complements that used in the former. Our result is a generalization of Jarzynski-Wòjcik heat fluctuation theorem.

Stochastic thermodynamics based on incomplete information: generalized Jarzynski equality with measurement errors with or without feedback

In the derivation of fluctuation relations, and in stochastic thermodynamics in general, it is tacitly assumed that we can measure the system perfectly, i.e., without measurement errors. We here demonstrate for a driven system immersed in a single heat bath, for which the classic Jarzynski equality holds, how to relax this assumption. Based on a general measurement model akin to Bayesian inference we derive a general expression for the fluctuation relation of the measured work and we study the case of an overdamped Brownian particle and of a two-level system in particular. We then generalize our results further and incorporate feedback in our description. We show and argue that, if measurement errors are fully taken into account by the agent who controls and observes the system, the standard Jarzynski–Sagawa–Ueda relation should be formulated differently. We again explicitly demonstrate this for an overdamped Brownian particle and a two-level system where the fluctuation relation of the measured work differs significantly from the efficacy parameter introduced by Sagawa and Ueda. Instead, the generalized fluctuation relation under feedback control, , holds only for a superobserver having perfect access to both the system and detector degrees of freedom, independently of whether or not the detector yields a noisy measurement record and whether or not we perform feedback.

Analogy between gambling and measurement-based work extraction

In information theory, one area of interest is gambling, where mutual information characterizes the maximal gain in wealth growth rate due to knowledge of side information; the betting strategy that achieves this maximum is named the Kelly strategy. In the field of physics, it was recently shown that mutual information can characterize the maximal amount of work that can be extracted from a single heat bath using measurement-based control protocols, i.e. using ‘information engines’. However, to the best of our knowledge, no relation between gambling and information engines has been presented before. In this paper, we briefly review the two concepts and then demonstrate an analogy between gambling, where bits are converted into wealth, and information engines, where bits representing measurements are converted into energy. From this analogy follows an extension of gambling to the continuous-valued case, which is shown to be useful for investments in currency exchange rates or in the stock market using options. Moreover, the analogy enables us to use well-known methods and results from one field to solve problems in the other. We present three such cases: maximum work extraction when the probability distributions governing the system and measurements are unknown, work extraction when some energy is lost in each cycle, e.g. due to friction, and an analysis of systems with memory. In all three cases, the analogy enables us to use known results in order to obtain new ones.

Optimal tuning of a confined Brownian information engine.

A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time τ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any τ. We find that the extracted work per engine cycle is maximum when τ approaches infinity, while the power is maximum when τ approaches zero.

The thermodynamic cost of driving quantum systems by their boundaries.

The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.