Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential.

Multistability, i.e., the coexistence of several attractors for a given set of system parameters, is one of the most important phenomena occurring in dynamical systems. We consider it in the velocity dynamics of a Brownian particle, driven by thermal fluctuations and moving in a biased periodic potential. In doing so, we focus on the impact of ergodicity-A concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and, as a consequence, the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken, and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperatures the ergodicity is, in principle, restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperatures, the multistability is robust with respect to the choice of the starting position and velocity of the particle.

Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond.

The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.

Quasi-stationary states of game-driven systems: A dynamical approach.

Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two complementary approaches to modeling evolution of player populations. The first addresses essentially finite populations by implementing the apparatus of Markov chains. The second assumes that the populations are infinite and operates with a system of mean-field deterministic differential equations. By using a model of two antagonistic populations, which are playing a game with stationary or periodically varying payoffs, we demonstrate that it exhibits metastable dynamics that is reducible neither to an immediate transition to a fixation (extinction of all but one strategy in a finite-size population) nor to the mean-field picture. In the case of stationary payoffs, this dynamics can be captured with a system of stochastic differential equations and interpreted as a stochastic Hopf bifurcation. In the case of varying payoffs, the metastable dynamics is much more complex than the dynamics of the means.

Comment on "Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force".

In a recent paper [Phys. Rev. E 101, 050101(R) (2020)PREHBM2470-004510.1103/PhysRevE.101.050101] an attempt is presented to formulate the nonequilibrium thermodynamics of an open system in terms of the Hamiltonian of mean force. The purpose of the present comment is to clarify severe restrictions of this approach and to stress that recently noted ambiguities [Phys. Rev. E 94, 022143 (2016)PREHBM2470-004510.1103/PhysRevE.94.022143] of fluctuating thermodynamic potentials cannot be removed in the suggested way.

Diffusion of colloidal rods in corrugated channels.

In many natural and artificial devices diffusive transport takes place in confined geometries with corrugated boundaries. Such boundaries cause both entropic and hydrodynamic effects, which have been studied only for the case of spherical particles. Here we experimentally investigate the diffusion of particles of elongated shape confined in a corrugated quasi-two-dimensional channel. The elongated shape causes complex excluded-volume interactions between particles and channel walls which reduce the accessible configuration space and lead to novel entropic free-energy effects. The extra rotational degree of freedom also gives rise to a complex diffusivity matrix that depends on both the particle location and its orientation. We further show how to extend the standard Fick-Jacobs theory to incorporate combined hydrodynamic and entropic effects, so as, for instance, to accurately predict experimentally measured mean first passage times along the channel. Our approach can be used as a generic method to describe translational diffusion of anisotropic particles in corrugated channels.

Asymptotic Floquet states of a periodically driven spin-boson system in the nonperturbative coupling regime.

Being an exemplary model of open quantum system, the spin-boson model is widely employed in theoretical and experimental studies. Beyond the weak coupling limit, the spin-boson dynamics can be described by a time-nonlocal generalized master equation with a memory kernel accounting for the dissipative effects induced by the bosonic environment. When the spin is in addition modulated by an external time-periodic electromagnetic field, the interplay between dissipation and forcing provides a spectrum of nontrivial asymptotic states, especially so in the regime of nonlinear response. Here we implement the method for evaluating the dissipative Floquet dynamics of non-Markovian systems introduced in Magazzù et al. [Phys. Rev. A 96, 042103 (2017)2469-992610.1103/PhysRevA.96.042103] to obtain these nonequilibrium asymptotic states.

Publisher's Note: Quantum resonant activation [Phys. Rev. E 95, 042104 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.042104.

Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels.

In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick-Jacobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus shows that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.

Quantum resonant activation.

Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probability density function (pdf) displays a complex, multipeaked behavior, which depends crucially on the details of initial phase, frequency, and strength of the driving. As an interesting feature we find that the mean first passage time enters the resonant activation regime at a critical frequency ν^{*} which depends very weakly on the strength of the driving. Moreover, we provide the relation between the first passage time pdf and the statistics of residence times.

Merits and qualms of work fluctuations in classical fluctuation theorems.

Work is one of the most basic notions in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature ß, work fluctuations depicted by the variance of e^{-ßW} are also minimized by adiabatic work protocols. This general result indicates that, if the variance of e^{-ßW} diverges for an adiabatic work protocol, it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. Such divergence is hence not an isolated event and thus greatly impacts on the efficiency of using Jarzynski's equality to simulate free-energy differences. Theoretical results are illustrated in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.

Self-Polarizing Microswimmers in Active Density Waves.

An artificial microswimmer drifts in response to spatio-temporal modulations of an activating suspension medium. We consider two competing mechanisms capable of influencing its tactic response: angular fluctuations, which help it explore its surroundings and thus diffuse faster toward more active regions, and self-polarization, a mechanism inherent to self-propulsion, which tends to orient the swimmer's velocity parallel or antiparallel to the local activation gradients. We investigate, both numerically and analytically, the combined action of such two mechanisms. By determining their relative magnitude, we characterize the selective transport of artificial microswimmers in inhomogeneous activating media.

Open system trajectories specify fluctuating work but not heat.

Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated. Yet, even though the Hamiltonian of mean force uniquely determines the equilibrium phase space probability density of a strongly coupled open system, the knowledge of this probability density alone is insufficient to determine the Hamiltonian of mean force, needed in constructing the underlying statistical mechanics and thermodynamics. We demonstrate that under the assumption that the Hamiltonian of mean force is known, an extension of thermodynamic structures from the level of averaged quantities to fluctuating objects (i.e., a stochastic thermodynamics) is possible. However, such a construction undesirably also involves a vast ambiguity. This situation is rooted in the eminent lack of a physical guiding principle allowing us to distinguish a physically meaningful theory out of a multitude of other equally conceivable ones.

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.

Occurrence of discontinuities in the performance of finite-time quantum Otto cycles.

We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.

Chemotaxis of artificial microswimmers in active density waves.

Living microorganisms are capable of a tactic response to external stimuli by swimming toward or away from the stimulus source; they do so by adapting their tactic signal transduction pathways to the environment. Their self-motility thus allows them to swim against a traveling tactic wave, whereas a simple fore-rear asymmetry argument would suggest the opposite. Their biomimetic counterpart, the artificial microswimmers, also propel themselves by harvesting kinetic energy from an active medium, but, in contrast, lack the adaptive capacity. Here we investigate the transport of artificial swimmers subject to traveling active waves and show, by means of analytical and numerical methods, that self-propelled particles can actually diffuse in either direction with respect to the wave, depending on its speed and waveform. Moreover, chiral swimmers, which move along spiraling trajectories, may diffuse preferably in a direction perpendicular to the active wave. Such a variety of tactic responses is explained by the modulation of the swimmer's diffusion inside traveling active pulses.

Aspects of quantum work.

Various approaches of defining and determining work performed on a quantum system are compared. Any operational definition of work, however, must allow for two facts: first, that work characterizes a process rather than an instantaneous state of a system and, second, that quantum systems are sensitive to the interactions with a measurement apparatus. We compare different measurement scenarios on the basis of the resulting postmeasurement states and the according probabilities for finding a particular work value. In particular, we analyze a recently proposed work meter for the case of a Gaussian pointer state and compare it with the results obtained by two projective and, alternatively, two Gaussian measurements. In the limit of a strong effective measurement strength the work distribution of projective two energy measurements can be recovered. In the opposite limit the average of work becomes independent of any measurement. Yet the fluctuations about this value diverge. The performance of the work meter is illustrated by the example of a spin in a suddenly changing magnetic field.

Meaning of temperature in different thermostatistical ensembles.

Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical ensembles, focusing in particular on subtleties that arise when ensembles become non-equivalent. The 'mother' of all ensembles, the microcanonical ensemble, uses entropy and internal energy (the most fundamental, dynamically conserved quantity) to derive temperature as a secondary thermodynamic variable. Over the past century, some confusion has been caused by the fact that several competing microcanonical entropy definitions are used in the literature, most commonly the volume and surface entropies introduced by Gibbs. It can be proved, however, that only the volume entropy satisfies exactly the traditional form of the laws of thermodynamics for a broad class of physical systems, including all standard classical Hamiltonian systems, regardless of their size. This mathematically rigorous fact implies that negative 'absolute' temperatures and Carnot efficiencies more than 1 are not achievable within a standard thermodynamical framework. As an important offspring of microcanonical thermostatistics, we shall briefly consider the canonical ensemble and comment on the validity of the Boltzmann weight factor. We conclude by addressing open mathematical problems that arise for systems with discrete energy spectra.

Experimental control of transport resonances in a coherent quantum rocking ratchet.

The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose-Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport.

Boosting thermoelectric efficiency using time-dependent control.

Thermoelectric efficiency is defined as the ratio of power delivered to the load of a device to the rate of heat flow from the source. Till date, it has been studied in presence of thermodynamic constraints set by the Onsager reciprocal relation and the second law of thermodynamics that severely bottleneck the thermoelectric efficiency. In this study, we propose a pathway to bypass these constraints using a time-dependent control and present a theoretical framework to study dynamic thermoelectric transport in the far from equilibrium regime. The presence of a control yields the sought after substantial efficiency enhancement and importantly a significant amount of power supplied by the control is utilised to convert the wasted-heat energy into useful-electric energy. Our findings are robust against nonlinear interactions and suggest that external time-dependent forcing, which can be incorporated with existing devices, provides a beneficial scheme to boost thermoelectric efficiency.