Attainability of Carnot efficiency with autonomous engines

Overcoming power-efficiency tradeoff in a micro heat engine by engineered system-bath interactions

All real heat engines, be it conventional macro engines or colloidal and atomic micro engines, inevitably tradeoff efficiency in their pursuit to maximize power. This basic postulate of finite-time thermodynamics has been the bane of all engine design for over two centuries and all optimal protocols implemented hitherto could at best minimize only the loss in the efficiency. The absence of a protocol that allows engines to overcome this limitation has prompted theoretical studies to suggest universality of the postulate in both passive and active engines. Here, we experimentally overcome the power-efficiency tradeoff in a colloidal Stirling engine by selectively reducing relaxation times over only the isochoric processes using system bath interactions generated by electrophoretic noise. Our approach opens a window of cycle times where the tradeoff is reversed and enables the engine to surpass even their quasistatic efficiency. Our strategies finally cut loose engine design from fundamental restrictions and pave way for the development of more efficient and powerful engines and devices.

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes-which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.

Stochastic currents and efficiency in an autonomous heat engine

We experimentally demonstrate that a Brownian gyrator of a colloidal particle confined in a two-dimensional harmonic potential with different effective temperatures on orthogonal axes can work as an autonomous heat engine capable of extracting work from the heat bath, generated by an optical feedback trap. The results confirm the theoretically predicted thermodynamic currents and validate the attainability of Carnot efficiency as well as the trade-off relation between power and efficiency. We further show that current fluctuations and the entropy production rate are time independent in the steady state and their product near the Carnot efficiency is close to the lower bound of the thermodynamic uncertainty relation.

Time-Symmetric Current and Its Fluctuation Response Relation around Nonequilibrium Stalling Stationary State

We propose a time-symmetric counterpart of the current in stochastic thermodynamics named the time-symmetric current. This quantity is defined with empirical measures and thus is symmetric under time reversal, while its ensemble average reproduces the amount of the average current. We prove that this time-symmetric current satisfies the fluctuation-response relation in the conventional form but with sign inversion. Remarkably, this fluctuation-response relation holds not only around equilibrium states but also around nonequilibrium stationary states if observed currents stall. The obtained relation also serves as an experimental tool for probing the value of a bare transition rate by measuring only time-integrated empirical measures.

Power, efficiency, and fluctuations in steady-state heat engines

We consider the quality factor Q, which quantifies the trade-off between power, efficiency, and fluctuations in steady-state heat engines modeled by dynamical systems. We show that the nonlinear scattering theory, in both classical and quantum mechanics, sets the bound Q=3/8 when approaching the Carnot efficiency. On the other hand, interacting, nonintegrable, and momentum-conserving systems can achieve the value Q=1/2, which is the universal upper bound in linear response. This result shows that interactions are necessary to achieve the optimal performance of a steady-state heat engine.

Optimal Cycles for Low-Dissipation Heat Engines

We consider the optimization of a finite-time Carnot engine characterized by small dissipations. We bound the power with a simple inequality and show that the optimal strategy is to perform small cycles around a given working point, which can be, thus, chosen optimally. Remarkably, this optimal point is independent of the figure of merit combining power and efficiency that is being maximized. Furthermore, for a general class of dissipative dynamics the maximal power output becomes proportional to the heat capacity of the working substance. Since the heat capacity can scale supraextensively with the number of constituents of the engine, this enables us to design optimal many-body Carnot engines reaching maximum efficiency at finite power per constituent in the thermodynamic limit.

Work as a memory record

The possibility of a controlled manipulation with molecules at the nanoscale allows us to gain net work from thermal energy, although this seems to be in contradiction to the second law of thermodynamics. Any manipulation, however, causes some memory records somewhere in the system's surroundings. To complete the thermodynamic cycle, these records must be reset, which costs energy that cancels the previous gain. An important memory record may also be the final state of the work reservoir. This memory record is not reset. Nevertheless, it is rewritten and the associated memory erased whenever the state of the work reservoir is changed during the cycle repeating. The question is, what is the cost of this memory erasure. To answer it, we study a hypothetical cycle in which all memory records are reset except the state of the work reservoir alone, and the ensemble average of the work extracted from an equilibrium heat reservoir during this cycle, 〈W〉, is positive. It is shown that a strong information coupling of the system and the work reservoir then influences the system's dynamics so much that the cycle repeat may exhibit quite different behavior. Especially, it can run reversely and decrease energy in the work reservoir. It implies that even if the memory erasure is a natural part of the process, it costs energy in accord with information thermodynamics. At the nanoscale, this energy cost may manifest as a process obeying the fluctuation theorem.

Efficiency Bounds for Minimally Nonlinear Irreversible Heat Engines with Broken Time-Reversal Symmetry

We study the minimally nonlinear irreversible heat engines in which the time-reversal symmetry for the systems may be broken. The expressions for the power and the efficiency are derived, in which the effects of the nonlinear terms due to dissipations are included. We show that, as within the linear responses, the minimally nonlinear irreversible heat engines can enable attainment of Carnot efficiency at positive power. We also find that the Curzon-Ahlborn limit imposed on the efficiency at maximum power can be overcome if the time-reversal symmetry is broken.

Unattainability of Carnot efficiency in thermal motors: Coarse graining and entropy production of Feynman-Smoluchowski ratchets

We revisit and analyze the thermodynamic efficiency of the Feynman-Smoluchowski (FS) ratchet, a classical thought experiment describing an autonomous heat-work converter. Starting from the full kinetics of the FS ratchet and deriving the exact forms of the hidden dissipations resulting from coarse graining, we restate the historical controversy over its thermodynamic efficiency. The existence of hidden entropy productions implies that the standard framework of stochastic thermodynamics applied to the coarse-grained descriptions fails in capturing the dissipative feature of the system. In response to this problem, we explore an extended framework of stochastic thermodynamics to reconstruct the hidden entropy production from the coarse-grained dynamics. The approach serves as a key example of how we can systematically address the problem of thermodynamic efficiency in a multivariable fluctuating nonequilibrium system.

Universal Trade-Off between Power, Efficiency, and Constancy in Steady-State Heat Engines

Heat engines should ideally have large power output, operate close to Carnot efficiency and show constancy, i.e., exhibit only small fluctuations in this output. For steady-state heat engines, driven by a constant temperature difference between the two heat baths, we prove that out of these three requirements only two are compatible. Constancy enters quantitatively the conventional trade-off between power and efficiency. Thus, we rationalize and unify recent suggestions for overcoming this simple trade-off. Our universal bound is illustrated for a paradigmatic model of a quantum dot solar cell and for a Brownian gyrator delivering mechanical work against an external force.

The underdamped Brownian duet and stochastic linear irreversible thermodynamics

Building on our earlier work [Proesmans et al., Phys. Rev. X 6, 041010 (2016)], we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss the Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.

Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound

A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.

Stationary engines in and beyond the linear response regime at the Carnot efficiency

The condition for stationary engines to attain the Carnot efficiency in and beyond the linear response regime is investigated. We find that this condition for finite-size engines is significantly different from that for macroscopic engines in the thermodynamic limit. For the case of finite-size engines, the tight-coupling condition in the linear response regime directly implies the attainability of the Carnot efficiency beyond the linear response regime. As opposed to this, for the case of macroscopic engines in the thermodynamic limit, there are three types of mechanisms to attain the Carnot efficiency. One mechanism allows engines to attain the Carnot efficiency only in the linear response limit, while the other two mechanisms enable engines to attain the Carnot efficiency beyond the linear response regime. These three mechanisms are classified by introducing a tight-coupling window.