Thermal bath engineering for swift equilibration

Harnessing Viscoelasticity to Suppress Irreversibility Buildup in a Colloidal Stirling Engine

Typically, the rate at which a heat engine can produce useful work is constrained by the buildup of irreversibility with increasing operating speed. Here, using a recently developed reservoir engineering technique, we designed and quantified the performance of a colloidal Stirling engine operating in a viscoelastic bath. While the bath acts like a viscous fluid in the quasistatic limit, and the engine's performance agrees with equilibrium predictions, on reducing the cycle time to the bath's structural relaxation time, the increasingly elastic response of the bath aids suppress the buildup of irreversibility. We show that the elastic energy stored during the isothermal compression step of the Stirling cycle facilitates quick equilibration in the isothermal expansion step. This results in equilibriumlike efficiencies even for cycle times shorter than the equilibration time of the colloidal particle.

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.

Optimal Time-Entropy Bounds and Speed Limits for Brownian Thermal Shortcuts

By controlling the variance of the radiation pressure exerted on an optically trapped microsphere in real time, we engineer temperature protocols that shortcut thermal relaxation when transferring the microsphere from one thermal equilibrium state to another. We identify the entropic footprint of such accelerated transfers and derive optimal temperature protocols that either minimize the production of entropy for a given transfer duration or accelerate the transfer for a given entropic cost as much as possible. Optimizing the trade-off yields time-entropy bounds that put speed limits on thermalization schemes. We further show how optimization expands the possibilities for accelerating Brownian thermalization down to its fundamental limits. Our approach paves the way for the design of optimized, finite-time thermodynamics for Brownian engines. It also offers a platform for investigating fundamental connections between information geometry and finite-time processes.

Shortcuts to Equilibrium with a Levitated Particle in the Underdamped Regime

We report on speeding-up equilibrium recovery in the previously unexplored general case of the underdamped regime using an optically levitated particle. We accelerate the convergence toward equilibrium by an order of magnitude compared to the natural relaxation time. We then discuss the efficiency of the studied protocols, especially for a multidimensional system. These results pave the way for optimizing realistic nanomachines with application to sensing and developing efficient nanoheat engines.

Information Engine in a Nonequilibrium Bath

Information engines can convert thermal fluctuations of a bath at temperature T into work at rates of order k_{B}T per relaxation time of the system. We show experimentally that such engines, when in contact with a bath that is out of equilibrium, can extract much more work. We place a heavy, micron-scale bead in a harmonic potential that ratchets up to capture favorable fluctuations. Adding a fluctuating electric field increases work extraction up to ten times, limited only by the strength of the applied field. Our results connect Maxwell's demon with energy harvesting and demonstrate that information engines in nonequilibrium baths can greatly outperform conventional engines.

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.

Optimal Control of Uniformly Heated Granular Fluids in Linear Response

We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously-from a mathematical point of view-prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.

Taming the Time Evolution in Overdamped Systems: Shortcuts Elaborated from Fast-Forward and Time-Reversed Protocols

Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution toward a well chosen common intermediate state, we analytically derive a smooth protocol to connect two arbitrary states in an arbitrarily short amount of time. Not only does the reverse-engineering approach proposed in this Letter contain the current-rather limited-catalog of explicit protocols, but it also provides a systematic strategy to build the connection between arbitrary states with a physically admissible driving. Optimization and further generalizations are also discussed.

Tuning the performance of a micrometer-sized Stirling engine through reservoir engineering

Colloidal heat engines are paradigmatic models to understand the conversion of heat into work in a noisy environment - a domain where biological and synthetic nano/micro machines function. While the operation of these engines across thermal baths is well-understood, how they function across baths with noise statistics that is non-Gaussian and also lacks memory, the simplest departure from the thermal case, remains unclear. Here we quantified the performance of a colloidal Stirling engine operating between an engineered memoryless non-Gaussian bath and a Gaussian one. In the quasistatic limit, the non-Gaussian engine functioned like a thermal one as predicted by theory. On increasing the operating speed, due to the nature of noise statistics, the onset of irreversibility for the non-Gaussian engine preceded its thermal counterpart and thus shifted the operating speed at which power is maximum. The performance of nano/micro machines can be tuned by altering only the nature of reservoir noise statistics.

Dynamical phase transition in the first-passage probability of a Brownian motion

We study the first-passage time distribution (FPTD) F(t_{f}|x_{0},L) for a freely diffusing particle starting at x_{0} in one dimension, to a target located at L, averaged over the initial position x_{0} drawn from a normalized distribution (1/σ)g(x_{0}/σ) of finite width σ. We show the averaged FPTD undergoes a sharp dynamical phase transition from a two-peak structure for b=L/σ>b_{c} to a single-peak structure for b<b_{c}. This transition is generated by the competition of two characteristic timescales σ^{2}/D and L^{2}/D, where D is the diffusion coefficient. A very good agreement is found between theoretical predictions and experimental results obtained with a Brownian bead whose diffusion is initialized by an optical trap which determines the initial distribution g(x_{0}/σ). We show that this transition is robust: It is present for all initial conditions with a finite σ, in all dimensions, and also exists for more general stochastic processes going beyond free diffusion.

Engineered swift equilibration for arbitrary geometries

Engineered swift equilibration (ESE) is a class of driving protocols that enforce an equilibrium distribution with respect to external control parameters at the beginning and end of rapid state transformations of open, classical nonequilibrium systems. ESE protocols have previously been derived and experimentally realized for Brownian particles in simple, one-dimensional, time-varying trapping potentials; one recent study considered ESE in two-dimensional Euclidean configuration space. Here we extend the ESE framework to generic, overdamped Brownian systems in arbitrary curved configuration space and illustrate our results with specific examples not amenable to previous techniques. Our approach may be used to impose the necessary dynamics to control the full temporal configurational distribution in a wide variety of experimentally realizable settings.

Engineered swift equilibration of a Brownian gyrator

In the context of stochastic thermodynamics, a minimal model for nonequilibrium steady states has been recently proposed: the Brownian gyrator (BG). It describes the stochastic overdamped motion of a particle in a two-dimensional harmonic potential, as in the classic Ornstein-Uhlenbeck process, but considering the simultaneous presence of two independent thermal baths. When the two baths have different temperatures, the steady BG exhibits a rotating current, a clear signature of nonequilibrium dynamics. Here, we consider a time-dependent potential, and we apply a reverse-engineering approach to derive exactly the required protocol to switch from an initial steady state to a final steady state in a finite time τ. The protocol can be built by first choosing an arbitrary quasistatic counterpart, with few constraints, and then adding a finite-time contribution which only depends upon the chosen quasistatic form and which is of order 1/τ. We also get a condition for transformations which, in finite time, conserve internal energy, useful for applications such as the design of microscopic thermal engines. Our study extends finite-time stochastic thermodynamics to transformations connecting nonequilibrium steady states.

Finite-Time Landauer Principle

We study the thermodynamic cost associated with the erasure of one bit of information over a finite amount of time. We present a general framework for minimizing the average work required when full control of a system's microstates is possible. In addition to exact numerical results, we find simple bounds proportional to the variance of the microscopic distribution associated with the state of the bit. In the short-time limit, we get a closed expression for the minimum average amount of work needed to erase a bit. The average work associated with the optimal protocol can be up to a factor of 4 smaller relative to protocols constrained to end in local equilibrium. Assessing prior experimental and numerical results based on heuristic protocols, we find that our bounds often dissipate an order of magnitude less energy.

Persistent random motion with maximally correlated fluctuations

How often should a random walker change its direction of motion in order to maximize correlation in velocity fluctuations over a finite time interval? We address this optimal diffusion problem in the context of the one-dimensional persistent random walk, where we evaluate the correlation and mutual information in velocity trajectories as a function of the persistence level and the observation time. We find the optimal persistence level corresponds to the average number of direction reversals asymptotically scaling as the square root of the observation time. This square-root scaling law makes the relative growth between the average number of direction reversals and the persistence length invariant with respect to changes in the overall time duration of the random walk.

Optimal work in a harmonic trap with bounded stiffness

We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness κ. We work out the optimal time dependence κ(t) by minimizing the work performed on the particle under the nonholonomic constraint 0≤κ≤κ_{max}, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analyzed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time t_{f} and the desired compression ratio κ_{f}/κ_{i}, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimization of heat engines.