Viktor Holubec - Academia.edu (original) (raw)

Papers by Viktor Holubec

Journal of physics. A, Mathematical and theoretical, Jul 9, 2024

Title: Nonequilibrium Thermodynamics of Small Systems Author: Viktor Holubec Department: Institut... more Title: Nonequilibrium Thermodynamics of Small Systems Author: Viktor Holubec Department: Institute of Theoretical Physics Supervisor: Doc. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: We investigate a microscopic engine based on an externally controlled two-level system. One cycle of the engine operation consists of two strokes. Within each stroke, the two energy levels are driven with a time-independent rate. The occupation probabilities of the two levels are controlled by the underlying Pauli rate equation and they represent the (delayed) system response in respect to the external driving. We give the exact solution of the dynamical equation and discuss its thermodynamical consequences. In between, we investigate the engine's efficiency, the power output, and the performance dependence on the control parameters. Secondly, we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two levels and the work done on the system during the previous evolution. Our exact calculation of the evolution operator for the augmented process allows for a detailed discussion of the probability density for the work done during the cycle of the engine operation. In the strongly irreversible regime, the density exhibits important..

arXiv (Cornell University), May 24, 2022

Retardation between sensation and action is an inherent biological trait. Here we study its effec... more Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that: (i) a discrete time delay in the orientational interactions diminishes the ability of strongly aligned swarms to follow a leader and, in return, increases their stability against random orientation fluctuations; (ii) both longer delays and higher speeds favor ballistic over diffusive spreading of information (orientation) through the swarm; (iii) for short delays, the mean change in the total orientation (the order parameter) scales linearly in a small orientational bias of the leaders and inversely in the delay time, while its variance first increases and then saturates with increasing delays; (iv) the linear response breaks down when orientation conservation is broken.

Description of stochastic motion of a particle in an unstable potential is a challenging topic si... more Description of stochastic motion of a particle in an unstable potential is a challenging topic since even small number of diverging trajectories leads to undefined statistic moments of particle position. This breaks down the standard statistical analysis of unstable mechanical processes and their applications. Therefore, we employ a different approach taking advantage of the local characteristics of the most-likely particle motion instead of the average motion. We experimentally verify theoretical predictions for a Brownian particle moving near an inflection in a cubic optical potential. Notably, the most-likely position of the particle atypically shifts against the force despite the trajectories diverge in opposite direction. In this work we study the influence of the analytical formula used for quantification of the most likely particle position parameters in the case where only limited number of trajectories is available.

Physical review, Jul 21, 2022

Physical interactions generally respect certain symmetries, such as reciprocity and energy conser... more Physical interactions generally respect certain symmetries, such as reciprocity and energy conservation, which survive in coarse grained isothermal descriptions. Active many-body systems usually break such symmetries intrinsically, on the particle level, so that their collective behavior is often more naturally interpreted as a result of information exchange. Here, we study numerically how information spreads from a "leader" particle through an initially aligned flock, described by the Vicsek model without noise. In the low-speed limit of a static spin lattice, we find purely conductive spreading, reminiscent of heat transfer. Swarm motility and heterogeneity can break reciprocity and spin conservation. But what seems more consequential for the swarm response is that the dispersion relation acquires a significant convective contribution along the leader's direction of motion.

Physical review, Feb 25, 2022

We derive an analytical expression for maximum efficiency at fixed power of heat pumps operating ... more We derive an analytical expression for maximum efficiency at fixed power of heat pumps operating along a finite-time reverse Carnot cycle under the low-dissipation assumption. The result is cumbersome, but it implies simple formulas for tight upper and lower bounds on the maximum efficiency and various analytically tractable approximations. In general, our results qualitatively agree with those obtained earlier for endoreversible heat pumps. In fact, we identify a special parameter regime when the performance of the low-dissipation and endoreversible devices is the same. At maximum power, heat pumps operate as work to heat converters with efficiency 1. Expressions for maximum efficiency at given power can be helpful in the identification of more practical operation regimes.

Journal of Statistical Mechanics: Theory and Experiment, Nov 15, 2012

We investigate the dynamics of a single-ended N-state molecular zipper based on a model originall... more We investigate the dynamics of a single-ended N-state molecular zipper based on a model originally proposed by Kittel. The molecule is driven unidirectionally towards the completely unzipped state with increasing time t. The driving lowers the energies of states with k unzipped links by an amount proportional to kt. We solve the Pauli rate equation for the state probabilities and the partial differential equations, which yield the probability distributions for the work performed on the zipper and for the heat exchanged with the thermal reservoir. Similarly to the related equilibrium model, two different regimes can be identified at a given temperature with respect to released molecular degrees of freedom per broken bond. In these two regimes the time evolution of the state probabilities as well as of the work and heat distributions show a qualitatively different behavior.

Journal of Physics A, Jun 17, 2020

We derive an exact expression for the probability density of work done on a particle that diffuse... more We derive an exact expression for the probability density of work done on a particle that diffuses in a parabolic potential with a stiffness varying by an arbitrary piecewise constant protocol. Based on this result, the work distribution for time-continuous protocols of the stiffness can be determined up to any degree of accuracy. This is achieved by replacing the continuous driving by a piecewise constant one with a number n of positive or negative steps of increasing or decreasing stiffness. With increasing n, the work distributions for the piecewise protocols approach that for the continuous protocol. The moment generating function of the work is given by the inverse square root of a polynomial of degree n, whose coefficients are efficiently calculated from a recurrence relation. The roots of the polynomials are real and positive (negative) steps of the protocol are associated with negative (positive) roots. Using these properties the inverse Laplace transform of the moment generating function is carried out explicitly. Fluctuation theorems are used to derive further properties of the polynomials and their roots.

Journal of Statistical Mechanics: Theory and Experiment, Mar 4, 2010

We investigate a microscopic motor based on an externally controlled two-level system. One cycle ... more We investigate a microscopic motor based on an externally controlled two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two-level system is in contact with a given thermal bath and its energy levels are driven with a constant rate. The time evolution of the occupation probabilities of the two states are controlled by one rate equation and represent the system's response with respect to the external driving. We give the exact solution of the rate equation for the limit cycle and discuss the emerging thermodynamics: the work done on the environment, the heat exchanged with the baths, the entropy production, the motor's efficiency, and the power output. Furthermore we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. The exact calculation of the evolution operator for the augmented process allows us to discuss in detail the probability density for the performed work during the limit cycle. In the strongly irreversible regime, the density exhibits important qualitative differences with respect to the more common Gaussian shape in the regime of weak irreversibility.

Physical review, Dec 10, 2020

Active Brownian engines rectify energy from reservoirs composed of self-propelling nonequilibrium... more Active Brownian engines rectify energy from reservoirs composed of self-propelling nonequilibrium molecules into work. We consider a class of such engines based on an underdamped Brownian particle trapped in a power-law potential. The energy they transform has thermodynamic properties of heat only if the non-equilibrium reservoir can be assigned a suitable effective temperature consistent with the second law and thus yielding an upper bound on the engine efficiency. The effective temperature exists if the total force exerted on the particle by the bath is not correlated with the particle position. In general, this occurs if the noise autocorrelation function and the friction kernel are proportional as in the fluctuation-dissipation theorem. But even if the proportionality is broken, the effective temperature can be defined in restricted, fine-tuned, parameter regimes, as we demonstrate on a specific example with harmonic potential.

Physical review, Mar 11, 2019

Physical Review Letters, Dec 3, 2018

Stochastic motion of particles in a highly unstable potential generates a number of diverging tra... more Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard statistical analysis of unstable mechanical processes and their applications. A newly proposed approach takes advantage of the local characteristics of the most probable particle motion instead of the divergent averages. We experimentally verify its theoretical predictions for a Brownian particle moving near an inflection in a highly unstable cubic optical potential. The most-likely position of the particle atypically shifts against the force despite the trajectories diverge in the opposite direction. The local uncertainty around the most-likely position saturates even for strong diffusion and enables well-resolved position detection. Remarkably, the measured particle distribution quickly converges to the quasi-stationary one with the same atypical shift for different initial particle positions. The demonstrated experimental confirmation of the theoretical predictions approves the utility of local characteristics for highly unstable systems which can be exploited in thermodynamic processes to uncover energetics of unstable systems.

Physical Review Letters, Sep 17, 2018

According to the laws of thermodynamics, no heat engine can beat the efficiency of a Carnot cycle... more According to the laws of thermodynamics, no heat engine can beat the efficiency of a Carnot cycle. This efficiency traditionally comes with vanishing power output and practical designs, optimized for power, generally achieve far less. Recently, various strategies to obtain Carnot's efficiency at large power were proposed. However, a thermodynamic uncertainty relation implies that steady-state heat engines can operate in this regime only at the cost of large fluctuations that render them immensely unreliable. Here, we demonstrate that this unfortunate trade-off can be overcome by designs operating cyclically under quasi-static conditions. The experimentally relevant yet exactly solvable model of an overdamped Brownian heat engine is used to illustrate the formal result. Our study highlights that work in cyclic heat engines and that in quasi-static ones are different stochastic processes.

Physica Scripta, Oct 1, 2015

The work distribution of a driven Brownian particle in an anharmonic potential is studied. The po... more The work distribution of a driven Brownian particle in an anharmonic potential is studied. The potential consists of two components: a harmonic part with a time-dependent stiffness and a time-independent logarithmic part. For arbitrary driving of the stiffness, the problem of solving the evolution equation for the joint probability density of work and particle position reduces to the solution of a Riccati differential equation. For a particular driving protocol, the Riccati equation can be solved and the exact large-work representation of the work distribution can be calculated. We propose a general form of the tail behavior. The asymptotic analysis of the work distribution is of vital importance for obtaining equilibrium free energy differences in experiments based on the Jarzynski identity. In the absence of the logarithmic component, our results agree with the work distribution for driven Brownian motion in a harmonic potential.

ACS Nano, Feb 8, 2021

A cornerstone of the directed motion of microscopic self-propelling particles is an asymmetric pa... more A cornerstone of the directed motion of microscopic self-propelling particles is an asymmetric particle structure defining a polarity axis along which these tiny machines move. This structural asymmetry ties the orientational Brownian motion to the microswimmers directional motion, limiting their persistence and making the long time motion effectively diffusive. Here, we demonstrate a completely symmetric thermoplasmonic microswimmer, which is propelled by laser-induced self-thermophoresis. The propulsion direction is imprinted externally to the particle by the heating laser position. The orientational Brownian motion, thus, becomes irrelevant for the propulsion, allowing enhanced control over the particles dynamics with almost arbitrary steering capability. We characterize the particle motion in experiments and simulations and also theoretically. The analysis reveals additional noise appearing in these systems, which is conjectured to be relevant for biological systems. Our experimental results show that even very small particles can be precisely controlled, enabling more advanced applications of these micromachines.

Science robotics, Mar 17, 2021

arXiv (Cornell University), Jul 31, 2021

At the dawn of thermodynamics, Carnot's constraint on efficiency of heat engines stimulated the f... more At the dawn of thermodynamics, Carnot's constraint on efficiency of heat engines stimulated the formulation of one of the most universal physical principles, the second law of thermodynamics. In recent years, the field of heat engines acquired a new twist due to enormous efforts to develop and describe microscopic machines based on systems as small as single atoms. At microscales, fluctuations are an inherent part of dynamics and thermodynamic variables such as work and heat fluctuate. Novel probabilistic formulations of the second law imply general symmetries and limitations for the fluctuating output power and efficiency of the small heat engines. Will their complete understanding ignite a similar revolution as the discovery of the second law? Here, we review the known general results concerning fluctuations in the performance of small heat engines. To make the discussion more transparent, we illustrate the main abstract findings on exactly solvable models and provide a thorough theoretical introduction for newcomers to the field.

arXiv (Cornell University), Dec 15, 2013

DNA hairpin molecules with periodic base sequences can be expected to exhibit a regular coarse-gr... more DNA hairpin molecules with periodic base sequences can be expected to exhibit a regular coarse-grained free energy landscape (FEL) as function of the number of open base pairs and applied mechanical force. Using a commonly employed model, we first analyse for which types of sequences a particularly simple landscape structure is predicted, where forward and backward energy barriers between partly unfolded states are decreasing linearly with force. Stochastic unfolding trajectories for such molecules with simple FEL are subsequently generated by kinetic Monte Carlo simulations. Introducing probabilities that can be sampled from these trajectories, it is shown how the parameters characterising the FEL can be estimated. Already 300 trajectories, as typically generated in experiments, provide faithful results for the FEL parameters.

EPL, Apr 13, 2023

Autonomous active Brownian ratchets rectify active Brownian particle motion solely by means of a ... more Autonomous active Brownian ratchets rectify active Brownian particle motion solely by means of a spatially modulated but stationary activity, without external forces. We argue that such ratcheting requires at least a two-dimensional geometry. The underlying principle is similar to the ratcheting induced by steric obstacles in microswimmer baths: suitably polarized swimmers get channeled, while the others get trapped in low-activity regions until they lose direction. The maximum current is generally reached in the limit of large propulsion speeds, in which the rectification efficiency vanishes. Maximum efficiency is attained at intermediate activities and numerically found to be on the order of a few percent, for ratchets with simple wedge-shaped low-activity regions.

Journal of Physics A, Dec 15, 2021