Efficiency of single-particle engines

Work distribution for unzipping processes

A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature T and subject to an external force f, which couples to the free length L of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force f_{c}(T) in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature T and force f, the full distribution P(L) of free lengths in the thermodynamic limit and show that it is qualitatively very different for ff_{c}. Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained P(L) already allows us to derive an analytical expression for the work distribution P(W) in the zipped phase f Collapse

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Affiliation(s)

Peter Werner Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
Alexander K Hartmann Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
Satya N Majumdar Laboratoire de Physique Théorique et Modèles Statistique, Université Paris-Saclay, 91405 Orsay CEDEX, France

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Thermodynamics of a minimal interacting heat engine: Comparison between engine designs

Collective effects stemming from many interacting units have attracted remarkable recent interest, not only for their presence in several systems in nature but also for the possibility of being used for the construction of efficient engine setups. Notwithstanding, little is known about the influence of the engine design, and most studies are restricted to the simplest cases (e.g., simultaneous contact with two thermal baths), not necessarily constituting a realistic setup implementation. In order to investigate the design and its influence on the performance, we introduce the collisional also referred as sequential description for a minimal model for interacting heat engines, composed of two coupled nanomachines placed in contact with a distinct thermal reservoir and subjected to a nonequilibrium work source at each stage. Thermodynamic quantities are exactly obtained irrespective of the model details. Distinct kinds of work sources are investigated and the influence of the interaction, temperature, period, and time asymmetry has been undertaken. Results show that a careful design of interaction provides superior performance than the interactionless case, including optimal power outputs and efficiencies at maximum power greater than known bounds or even the system presenting efficiencies close to the ideal (Carnot) limit. As a complementary analysis, we also show that the case of the system simultaneously placed in contact with two thermal reservoirs constitutes a particular case of our framework.

Obtaining efficient collisional engines via velocity-dependent drivings

Brownian particles interacting sequentially with distinct temperatures and driving forces at each stroke have been tackled as a reliable alternative for the construction of engine setups. However, they can behave very inefficiently depending on the driving used for the work source and/or when temperatures of each stage are very different from each other. Inspired by some models for molecular motors and recent experimental studies, a coupling between driving and velocities is introduced and detail investigated from stochastic thermodynamics. Exact expressions for thermodynamic quantities and distinct maximization routes have been obtained. The search of an optimal coupling provides a substantial increase of engine performance (mainly efficiency), even for large ΔT. A simple and general argument for the optimal coupling can be estimated, irrespective of the driving and other model details.

Thermodynamics and efficiency of sequentially collisional Brownian particles: The role of drivings

Brownian particles placed sequentially in contact with distinct thermal reservoirs and subjected to external driving forces are promising candidates for the construction of reliable engine setups. In this contribution, we address the role of driving forces for enhancing the collisional machine performance. Analytical expressions for thermodynamic quantities such as power output and efficiency are obtained for general driving schemes. A proper choice of these driving schemes substantially increases both power output and efficiency and extends the working regime. Maximizations of power and efficiency, whether with respect to the strength of the force, driving scheme, or both have been considered and exemplified for two kind of drivings: generic power-law and harmonic (sinusoidal) drivings.

One-particle engine with a porous piston

We propose a variation of the classical Szilard engine that uses a porous piston. Such an engine requires neither information about the position of the particle, nor the removal and subsequent insertion of the piston when resetting the engine to continue doing work by lifting a mass against a gravitational field. Though the engine operates in contact with a single thermal reservoir, the reset mechanism acts as a second reservoir, dissipating energy when a mass that has been lifted by the engine is removed to initiate a new operation cycle.

Obtaining efficient thermal engines from interacting Brownian particles under time-periodic drivings

We introduce an alternative route for obtaining reliable cyclic engines, based on two interacting Brownian particles under time-periodic drivings which can be used as a work-to-work converter or a heat engine. Exact expressions for the thermodynamic fluxes, such as power and heat, are obtained using the framework of stochastic thermodynamic. We then use these exact expression to optimize the driving protocols with respect to output forces, their phase difference. For the work-to-work engine, they are solely expressed in terms of Onsager coefficients and their derivatives, whereas nonlinear effects start to play a role since the particles are at different temperatures. Our results suggest that stronger coupling generally leads to better performance, but careful design is needed to optimize the external forces.

Efficiency Fluctuations of Stochastic Machines Undergoing a Phase Transition

We study the efficiency fluctuations of a stochastic heat engine made of N interacting unicyclic machines and undergoing a phase transition in the macroscopic limit. Depending on N and on the observation time, the machine can explore its whole phase space or not. This affects the engine efficiency that either strongly fluctuates on a large interval of equiprobable efficiencies (ergodic case) or fluctuates close to several most likely values (nonergodic case). We also provide a proof that despite the phase transition, the decay rate of the efficiency distribution at the reversible efficiency remains largest one although other efficiencies can now decay equally fast.

Thermodynamic Cost and Benefit of Memory

This Letter exposes a tight connection between the thermodynamic efficiency of information processing and predictive inference. A generalized lower bound on dissipation is derived for partially observable information engines which are allowed to use temperature differences. It is shown that the retention of irrelevant information limits efficiency. A data representation method is derived from optimizing a fundamental physical limit to information processing: minimizing the lower bound on dissipation leads to a compression method that maximally retains relevant, predictive, information. In that sense, predictive inference emerges as the strategy that least precludes energy efficiency.

Efficiency Fluctuations in Microscopic Machines

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a "universal theory of efficiency fluctuations" at long times, for machines with a finite state space, was developed by Verley et al. [Nat. Commun. 5, 4721 (2014)NCAOBW2041-172310.1038/ncomms5721; Phys. Rev. E 90, 052145 (2014)PRESCM1539-375510.1103/PhysRevE.90.052145]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the "universal features" and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two nontrivial models of colloidal engines.

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.

Molecular kinetic analysis of a local equilibrium Carnot cycle

We identify a velocity distribution function of ideal gas particles that is compatible with the local equilibrium assumption and the fundamental thermodynamic relation satisfying the endoreversibility. We find that this distribution is a Maxwell-Boltzmann distribution with a spatially uniform temperature and a spatially varying local center-of-mass velocity. We construct the local equilibrium Carnot cycle of an ideal gas, based on this distribution, and show that the efficiency of the present cycle is given by the endoreversible Carnot efficiency using the molecular kinetic temperatures of the gas. We also obtain an analytic expression of the efficiency at maximum power of our cycle under a small temperature difference. Our theory is also confirmed by a molecular dynamics simulation.

Stochastic Thermodynamics of a Particle in a Box

The piston system (particles in a box) is the simplest paradigmatic model in traditional thermodynamics. However, the recently established framework of stochastic thermodynamics (ST) fails to apply to this model system due to the embedded singularity in the potential. In this Letter, we study the ST of a particle in a box by adopting a novel coordinate transformation technique. Through comparing with the exact solution of a breathing harmonic oscillator, we obtain analytical results of work distribution for an arbitrary protocol in the linear response regime and verify various predictions of the fluctuation-dissipation relation. When applying to the Brownian Szilard engine model, we obtain the optimal protocol λ_{t}=λ_{0}2^{t/τ} for a given sufficiently long total time τ. Our study not only establishes a paradigm for studying ST of a particle in a box but also bridges the long-standing gap in the development of ST.

Thermodynamics of slow solutions to the gas-piston equations

Despite its historical importance, a perfect gas enclosed by a pistons and in contact with a thermal reservoirs is a system still largely under study. Its thermodynamic properties are not yet well understood when driven under nonequilibrium conditions, and analytic formulas that describe the heat exchanged with the reservoir are rare. In this paper we prove a power series expansions for the heat when both the external force and the reservoir temperature are slowly varying over time but the overall process is not quasistatic. To do so, we use the dynamical equations from [Cerino et al., Phys. Rev. E 91, 032128 (2015)PLEEE81539-375510.1103/PhysRevE.91.032128] and an uncommon application of the regular perturbation technique.

Efficiency fluctuations of small machines with unknown losses

The efficiency statistics of a small thermodynamic machine has been recently investigated assuming that the total dissipation is a linear combination of two currents: the input and output currents. Here, we relax this standard assumption and consider the question of the efficiency fluctuations for a machine involving three different currents, first in full generality and second for two different examples. Since the third current may not be measurable and/or may decrease the machine efficiency, our motivation is to study the effect of unknown losses in small machines.

Linear and nonlinear thermodynamics of a kinetic heat engine with fast transformations

We investigate a kinetic heat engine model composed of particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period τ: their relative excursions, δ and ε, respectively, constitute the thermodynamic forces dragging the system out of equilibrium. The analysis of the entropy production of the system allows us to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small δ and ε the fluxes are linear in the forces through a τ-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which-in the linear regime-yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e., outside of the linear regime. In all our analysis the adiabatic limit τ→∞ and the the small-force limit δ,ε→0 are not directly related.