Brownian motors in the microscale domain: enhancement of efficiency by noise

Absolute negative mobility of an inertial Brownian particle in an oscillating potential

Transport of an inertial Brownian particle in an oscillating potential is numerically investigated in the presence of an external constant force. The oscillating potential can break thermodynamic equilibrium. Within appropriate parameter regimes, the particle moves in a direction opposite to the constant force, which means that the system can exhibit the phenomenon of absolute negative mobility (ANM). Furthermore, it may be inferred from the bifurcation diagrams that ANM originates from chaotic-periodic transitions, where the particle subjected to a constant force performs reverse periodic motion due to continuous reverse driving by the oscillating potential. Based on GPU acceleration techniques, we present the distribution of ANM in the parameter space and analyze how the ANM depends on the system parameters. These results are robust in a wide range of parameters and may pave the way to the experimental realization of ANM.

Memory-induced absolute negative mobility

Non-Markovian systems form a broad area of physics that remains greatly unexplored despite years of intensive investigations. The spotlight is on memory as a source of effects that are absent in their Markovian counterparts. In this work, we dive into this problem and analyze a driven Brownian particle moving in a spatially periodic potential and exposed to correlated thermal noise. We show that the absolute negative mobility effect, in which the net movement of the particle is in the direction opposite to the average force acting on it, may be induced by the memory of the setup. To explain the origin of this phenomenon, we resort to the recently developed effective mass approach to dynamics of non-Markovian systems.

Effective mass approach to memory in non-Markovian systems

Recent pioneering experiments on non-Markovian dynamics done, e.g., for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still awaiting discovery. It is related to the fact that typically for simplification the Markovian approximation is employed and as a consequence the memory is neglected. Therefore, methods allowing to study memory effects are extremely valuable. We demonstrate that a non-Markovian system described by the Generalized Langevin Equation (GLE) for a Brownian particle of mass M can be approximated by the memoryless Langevin equation in which the memory effects are correctly reproduced solely via the effective mass M^{*} of the Brownian particle which is determined only by the form of the memory kernel. Our work lays the foundation for an impactful approach which allows one to readily study memory-related corrections to Markovian dynamics.

Mechanism for giant enhancement of transport induced by active fluctuations

Understanding the role of active fluctuations in physics is a problem in statu nascendi appearing both as a hot topic and a major challenge. The reason for this is the fact that they are inherently nonequilibrium. This feature opens a landscape of phenomena yet to be explored that are absent in the presence of thermal fluctuations alone. Recently a paradoxical effect has been briefly communicated in which a free-particle transport induced by active fluctuations in the form white Poisson shot noise can be enormously boosted when the particle is additionally subjected to a periodic potential. In this work we considerably extend the original predictions and investigate the impact of statistics of active noise on the occurrence of this effect. We construct a toy model of the jump-relaxation process that allow us to identify different regimes of the free-particle transport boost and explain their corresponding mechanisms. Moreover, we formulate and interpret the conditions for statistics of active fluctuations that are necessary for the emergence of giant enhancement of the free-particle transport induced by the periodic potential. Our results are relevant not only for microscopic physical systems but also for biological ones such as, e.g., living cells where fluctuations generated by metabolic activities are active by default.

Paradoxical nature of negative mobility in the weak dissipation regime

We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time-periodic force and a static bias. In doing so, we focus on the negative mobility phenomenon in which the average velocity of the particle is opposite to the constant force acting on it. Surprisingly, we find that in the weak dissipation regime, thermal fluctuations induce negative mobility much more frequently than it happens if dissipation is stronger. In particular, for the very first time, we report a parameter set in which thermal noise causes this effect in the nonlinear response regime. Moreover, we show that the coexistence of deterministic negative mobility and chaos is routinely encountered when approaching the overdamped limit in which chaos does not emerge rather than near the Hamiltonian regime of which chaos is one of the hallmarks. On the other hand, at non-zero temperature, the negative mobility in the weak dissipation regime is typically affected by weak ergodicity breaking. Our findings can be corroborated experimentally in a multitude of physical realizations, including, e.g., Josephson junctions and cold atoms dwelling in optical lattices.

Periodic potential can enormously boost free-particle transport induced by active fluctuations

Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with an active environment. They drive the system far from equilibrium and can induce phenomena that are forbidden at equilibrium states by, e.g., fluctuation-dissipation relations and detailed balance symmetry. Understanding their role in living matter is emerging as a challenge for physics. Here we demonstrate a paradoxical effect in which a free-particle transport induced by active fluctuations can be boosted by many orders of magnitude when the particle is additionally subjected to a periodic potential. In contrast, within the realm of only thermal fluctuations, the velocity of a free particle exposed to a bias is reduced when the periodic potential is switched on. The presented mechanism is significant for understanding nonequilibrium environments such as living cells, where it can explain from a fundamental point of view why spatially periodic structures known as microtubules are necessary to generate impressively effective intracellular transport. Our findings can be readily corroborated experimentally, e.g., in a setup comprising a colloidal particle in an optically generated periodic potential.

Giant oscillations of diffusion in ac-driven periodic systems

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is normal in the long time limit and exhibits intriguing giant damped quasiperiodic oscillations as a function of the external driving amplitude. As the mechanism behind this effect, we identify the corresponding oscillations of difference in the number of locked and running trajectories that carry the leading contribution to the diffusion coefficient. Our findings can be verified experimentally in a multitude of physical systems, including colloidal particles, Josephson junction, or cold atoms dwelling in optical lattices, to name only a few.

Dispersive transport dynamics in porous media emerge from local correlations

Understanding and controlling transport through complex media is central for a plethora of processes ranging from technical to biological applications. Yet, the effect of micro-scale manipulations on macroscopic transport dynamics still poses conceptual conundrums. Here, we demonstrate the predictive power of a conceptual shift in describing complex media by local micro-scale correlations instead of an assembly of uncorrelated minimal units. Specifically, we show that the non-linear dependency between microscopic morphological properties and macroscopic transport characteristics in porous media is captured by transport statistics on the level of pore junctions instead of single pores. Probing experimentally and numerically transport through two-dimensional porous media while gradually increasing flow heterogeneity, we find a non-monotonic change in transport efficiency. Using analytic arguments, we built physical intuition on how this non-monotonic dependency emerges from junction statistics. The shift in paradigm presented here broadly affects our understanding of transport within the diversity of complex media.

Dispersive transport through complex media, relevant for semiconductors, liquid crystals, and biological soft matter, is influenced by their microscopic, porous structure. The authors consider the statistics of pore-junction units, in contrast to individual pores, to link morphology and macroscopic transport characteristics.

Colossal Brownian yet non-Gaussian diffusion in a periodic potential: Impact of nonequilibrium noise amplitude statistics

Last year, Białas et al. [Phys. Rev. E 102, 042121 (2020)] studied an overdamped dynamics of nonequilibrium noise driven Brownian particle dwelling in a spatially periodic potential and discovered a novel class of Brownian, yet non-Gaussian diffusion. The mean square displacement of the particle grows linearly with time and the probability density for the particle position is Gaussian; however, the corresponding distribution for the increments is non-Gaussian. The latter property induces the colossal enhancement of diffusion, significantly exceeding the well known effect of giant diffusion. Here, we considerably extend the above predictions by investigating the influence of nonequilibrium noise amplitude statistics on the colossal Brownian, yet non-Gaussian diffusion. The tail of amplitude distribution crucially impacts both the magnitude of diffusion amplification and the Gaussianity of the position and increments statistics. Our results carry profound consequences for diffusive behavior in nonequilibrium settings such as living cells in which diffusion is a central transport mechanism.

Conundrum of weak-noise limit for diffusion in a tilted periodic potential

The weak-noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity, frequently hidden in deterministic systems, to give rise to phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically. We reinvestigate in this context the paradigmatic model of nonequilibrium statistical physics consisting of inertial Brownian particles diffusing in a tilted periodic potential by exploiting state-of-the-art computer simulations of an extremely long timescale. In contrast to previous results on this longstanding problem, we draw an inference that in the parameter regime for which the particle velocity is bistable the lifetime of ballistic diffusion diverges to infinity when the thermal noise intensity tends to zero, i.e., an everlasting ballistic diffusion emerges. As a consequence, the diffusion coefficient does not reach its stationary constant value.

Modeling and Performance Optimization of an Irreversible Two-Stage Combined Thermal Brownian Heat Engine

Based on finite time thermodynamics, an irreversible combined thermal Brownian heat engine model is established in this paper. The model consists of two thermal Brownian heat engines which are operating in tandem with thermal contact with three heat reservoirs. The rates of heat transfer are finite between the heat engine and the reservoir. Considering the heat leakage and the losses caused by kinetic energy change of particles, the formulas of steady current, power output and efficiency are derived. The power output and efficiency of combined heat engine are smaller than that of single heat engine operating between reservoirs with same temperatures. When the potential filed is free from external load, the effects of asymmetry of the potential, barrier height and heat leakage on the performance of the combined heat engine are analyzed. When the potential field is free from external load, the effects of basic design parameters on the performance of the combined heat engine are analyzed. The optimal power and efficiency are obtained by optimizing the barrier heights of two heat engines. The optimal working regions are obtained. There is optimal temperature ratio which maximize the overall power output or efficiency. When the potential filed is subjected to external load, effect of external load is analyzed. The steady current decreases versus external load; the power output and efficiency are monotonically increasing versus external load.

Tunable particle separation via deterministic absolute negative mobility

Particle isolation techniques are in the spotlight of many areas of science and engineering. In food industry, a harmful bacterial activity can be prevented with the help of separation schemes. In health care, isolation techniques are used to distinguish cancer and healthy cells or in therapy for Alzheimer's and Parkinson's diseases. We consider a cloud of Brownian particles of different sizes moving in a periodic potential and subjected to an unbiased driving as well as a constant force. We reveal an efficient separation strategy via the counterintuitive effect of negative mobility when particles of a given size are transported in a direction opposite to the applied constant force. We demonstrate a tunable separation solution in which size of the particle undergoing separation may be controlled by variation of the parameters of the external force applied to the system. This approach is an important step towards the development of point-of-care lab-on-a-chip devices.

Colossal Brownian yet non-Gaussian diffusion induced by nonequilibrium noise

We report on Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, and the probability density for the particle spreading is Gaussian like, but the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behavior is not a consequence of either a space- or time-dependent diffusivity, but is induced by external nonthermal noise acting on the particle dwelling in a periodic potential. The existence of the exponential tail in the increment statistics leads to colossal enhancement of diffusion, drastically surpassing the previously researched situation known as "giant" diffusion. This colossal diffusion enhancement crucially impacts a broad spectrum of the first arrival problems, such as diffusion limited reactions governing transport in living cells.

Efficient harmonic oscillator chain energy harvester driven by colored noise

We study the performance of an electromechanical harmonic oscillator chain as an energy harvester to extract power from finite-bandwidth ambient random vibrations, which are modelled by colored noise. The proposed device is numerically simulated and its performance assessed by means of the net electrical power generated and its efficiency in converting the external noise-supplied power into electrical power. Our main result is a much enhanced performance, both in the net electrical power delivered and in efficiency, of the harmonic chain with respect to the popular single oscillator resonator. Our numerical findings are explained by means of an analytical approximation, in excellent agreement with numerics.

Phase Dependent Vectorial Current Control in Symmetric Noisy Optical Ratchets

In this work, we demonstrate single microparticle transport in a symmetric noisy optical ratchet made with a linear array of 20 optical potentials, where each potential is a spatially symmetric low power (<2.5  mW) three-dimensional trap. Both the external force F(t) and the depth V_{0i}(t) of the optical potentials are dynamic and change at the same frequency ν=2  Hz. The depths of the individual optical potentials are random (uncorrelated noise) distributed around a mean value V_{0}, ⟨V_{0i}(t)⟩=V_{0}, while the external force is periodic and unbiased ⟨F(t)⟩=0. The system is completely symmetric for times t≫1/ν. Directed transport is possible as a result of the symmetry being broken at times on the order of 1/ν. We find that the direction and speed of motion (current) are coupled to the phase difference between the noise in the optical potentials and the external periodic force.

Spontaneous rectification and absolute negative mobility of inertial Brownian particles induced by Gaussian potentials in steady laminar flows

We study the transport of inertial Brownian particles in steady laminar flows in the presence of two-dimensional Gaussian potentials. Through extensive numerical simulations, it is found that the transport is sensitively dependent on the external constant force and the Gaussian potential. Within tailored parameter regimes, the system exhibits a rich variety of transport behaviors. There exists the phenomenon of spontaneous rectification (SR), where the directed transport of particles can occur in the absence of any external driving forces. It is found that SR of the particles can be manipulated by the spatial position of the Gaussian potential. Moreover, when the potential lies at the center of the cellular flow, the system exhibits absolute negative mobility (ANM), i.e., the particles can move in a direction opposite to the constant force. More importantly, the phenomenon of ANM induced by Gaussian potentials is robust in a wide range of system parameters and can be further strengthened with the optimized parameters, which may pave the way to the implementation of related experiments.

Thermodynamics and Steady State of Quantum Motors and Pumps Far from Equilibrium

In this article, we briefly review the dynamical and thermodynamical aspects of different forms of quantum motors and quantum pumps. We then extend previous results to provide new theoretical tools for a systematic study of those phenomena at far-from-equilibrium conditions. We mainly focus on two key topics: (1) The steady-state regime of quantum motors and pumps, paying particular attention to the role of higher order terms in the nonadiabatic expansion of the current-induced forces. (2) The thermodynamical properties of such systems, emphasizing systematic ways of studying the relationship between different energy fluxes (charge and heat currents and mechanical power) passing through the system when beyond-first-order expansions are required. We derive a general order-by-order scheme based on energy conservation to rationalize how every order of the expansion of one form of energy flux is connected with the others. We use this approach to give a physical interpretation of the leading terms of the expansion. Finally, we illustrate the above-discussed topics in a double quantum dot within the Coulomb-blockade regime and capacitively coupled to a mechanical rotor. We find many exciting features of this system for arbitrary nonequilibrium conditions: a definite parity of the expansion coefficients with respect to the voltage or temperature biases; negative friction coefficients; and the fact that, under fixed parameters, the device can exhibit multiple steady states where it may operate as a quantum motor or as a quantum pump, depending on the initial conditions.

Tunable Mass Separation via Negative Mobility

A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles and their mass value. We consider an inertial Brownian particle moving in a symmetric periodic potential and subjected to an externally applied unbiased harmonic driving in combination with a constant applied bias. In doing so, we identify a most efficient separation scheme which is based on the anomalous transport feature of negative mobility, meaning that the immersed particles move in the direction opposite to the acting bias. This work is the first of its kind in demonstrating a tunable separation mechanism in which the particle mass targeted for isolation is effectively controlled over a regime of nearly 2 orders of mass magnitude upon changing solely the frequency of the external harmonic driving. This approach may provide mass selectivity required in present and future separation of a diversity of nano- and microsized particles of either biological or synthetic origin.

SQUID ratchet: Statistics of transitions in dynamical localization

We study occupation of certain regions of phase space of an asymmetric superconducting quantum interference device (SQUID) driven by thermal noise, subjected to an external ac current and threaded by a constant magnetic flux. Thermally activated transitions between the states which reflect three deterministic attractors are analyzed in the regime of the noise induced dynamical localization of the Josephson phase velocity, i.e., there is a temperature interval in which the conditional probability of the voltage to remain in one of the states is very close to one. Implications of this phenomenon on the dc voltage drop across the SQUID are discussed. We detect the emergence of the power law tails in a residence time probability distribution of the Josephson phase velocity and discuss the role of symmetry breaking in dynamical localization induced by thermal noise. This phenomenon illustrates how deterministic-like behavior may be extracted from randomness by stochasticity itself. It reveals another face of noise.

Transport of active particles induced by wedge-shaped barriers in straight channels with hard and soft walls

The transport of active particles in straight channels is numerically investigated. The periodic wedge-shaped barriers can produce the asymmetry of the system and induce the directed transport of the active particles. The direction of the transport is determined by the apex angle of the wedge-shaped barriers. By confining the particles in channels with hard and soft walls, the transport exhibits similar behaviors. The average velocity is a peaked function of the translational diffusion, while it decreases monotonously with the increase of the rotational diffusion. Moreover, the simulation results show that the transport is sensitive to the parameters of the confined structures, such as the pore width, the intensity of potential, and the channel period.

Subdiffusion via dynamical localization induced by thermal equilibrium fluctuations

We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion is a long-living transient whose lifetime can be many, many orders of magnitude larger than characteristic time scales of the setup thus being amenable to experimental observations. As a reason for this subdiffusive behaviour in the coordinate space we identify thermal noise induced dynamical localization in the velocity (momentum) space. This novel idea is distinct from existing knowledge and has never been reported for any classical or quantum system. It suggests reconsideration of generally accepted opinion that subdiffusion is due to broad distributions or strong correlations which reflect disorder, trapping, viscoelasticity of the medium or geometrical constraints.

Performance optimization in two-dimensional Brownian rotary ratchet models

With a model for two-dimensional (2D) Brownian rotary ratchets being capable of producing a net torque under athermal random forces, its optimization for mean angular momentum (L), mean angular velocity (ω), and efficiency (η) is considered. In the model, supposing that such a small ratchet system is placed in a thermal bath, the motion of the rotor in the stator is described by the Langevin dynamics of a particle in a 2D ratchet potential, which consists of a static and a time-dependent interaction between rotor and stator; for the latter, we examine a force [randomly directed dc field (RDDF)] for which only the direction is instantaneously updated in a sequence of events in a Poisson process. Because of the chirality of the static part of the potential, it is found that the RDDF causes net rotation while coupling with the thermal fluctuations. Then, to maximize the efficiency of the power consumption of the net rotation, we consider optimizing the static part of the ratchet potential. A crucial point is that the proposed form of ratchet potential enables us to capture the essential feature of 2D ratchet potentials with two closed curves and allows us to systematically construct an optimization strategy. In this paper, we show a method for maximizing L, ω, and η, its outcome in 2D two-tooth ratchet systems, and a direction of optimization for a three-tooth ratchet system.

Noise-enabled optical ratchets

In this contribution, we report on the implementation of a novel noise-enabled optical ratchet system. We demonstrate that, unlike commonly-used ratchet schemes-where complex asymmetric optical potentials are needed-efficient transport of microparticles across a one-dimensional optical lattice can be produced by introducing controllable noise in the system. This work might open interesting routes towards the development of new technologies aimed at enhancing the efficiency of transport occurring at the micro- and nanoscale, from novel particle-sorting tools to efficient molecular motors.

Brownian ratchets: How stronger thermal noise can reduce diffusion

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

Tunable φ Josephson junction ratchet

We demonstrate experimentally the operation of a deterministic Josephson ratchet with tunable asymmetry. The ratchet is based on a φ Josephson junction with a ferromagnetic barrier operating in the underdamped regime. The system is probed also under the action of an additional dc current, which acts as a counterforce trying to stop the ratchet. Under these conditions the ratchet works against the counterforce, thus producing a nonzero output power. Finally, we estimate the efficiency of the φ Josephson junction ratchet.

Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases.

Noise-assisted energy transport in electrical oscillator networks with off-diagonal dynamical disorder

Noise is generally thought as detrimental for energy transport in coupled oscillator networks. However, it has been shown that for certain coherently evolving systems, the presence of noise can enhance, somehow unexpectedly, their transport efficiency; a phenomenon called environment-assisted quantum transport (ENAQT) or dephasing-assisted transport. Here, we report on the experimental observation of such effect in a network of coupled electrical oscillators. We demonstrate that by introducing stochastic fluctuations in one of the couplings of the network, a relative enhancement in the energy transport efficiency of 22.5 ± 3.6% can be observed.

Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling

The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.

Diffusion anomalies in ac-driven Brownian ratchets

We study diffusion in ratchet systems. As a particular experimental realization we consider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux. We analyze mean-square displacement of the Josephson phase and find that within selected parameter regimes it evolves in three distinct stages: initially as superdiffusion, next as subdiffusion, and finally as normal diffusion in the asymptotic long-time limit. We show how crossover times that separates these stages can be controlled by temperature and an external magnetic flux. The first two stages can last many orders longer than characteristic time scales of the system, thus being comfortably detectable experimentally. The origin of abnormal behavior is noticeable related to the ratchet form of the potential revealing an entirely new mechanism of emergence of anomalous diffusion. Moreover, a normal diffusion coefficient exhibits nonmonotonic dependence on temperature leading to an intriguing phenomenon of thermal noise suppressed diffusion. The proposed setup for experimental verification of our findings provides a new and promising testing ground for investigating anomalies in diffusion phenomena.

Josephson phase diffusion in the superconducting quantum interference device ratchet

We study diffusion of the Josephson phase in the asymmetric superconducting quantum interference device (SQUID) subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing so, we concentrate on the previously reported regime [J. Spiechowicz and J. Łuczka, New J. Phys. 17, 023054 (2015)] for which efficiency of the SQUID attains a global maximum. For long times, the mean-square displacement of the phase is a linear function of time, meaning that diffusion is normal. Its coefficient is small indicating rather regular phase evolution. However, it can be magnified several times by tailoring experimentally accessible parameters like amplitudes of the ac current or external magnetic flux. Finally, we prove that in the deterministic limit this regime is essentially non-chaotic and possesses an unexpected simplicity of attractors.

Efficiency statistics at all times: Carnot limit at finite power

We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter ζ. It has a peculiar behavior: no moments, one sub-, and one super-Carnot maxima corresponding to reverse operating regimes (engine or pump), the most probable efficiency decreasing in time. The limit ζ→0 where the Carnot bound can be saturated gives rise to two extreme situations, one where the machine works at its macroscopic efficiency, with Carnot limit corresponding to no entropy production, and one where for a transient time scaling like 1/ζ microscopic fluctuations are enhanced in such a way that the most probable efficiency approaches the Carnot limit at finite entropy production.