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Thermophoretic and Hydrodynamic Interactions in Artificial Active Matter
Kolář, Martin ; Holubec, Viktor (advisor) ; Tůma, Karel (referee)
The study of artificial active matter has significantly intensified in recent years due to its potential practical applications and promises to understand living organisms' in- teractions and collective behaviour. The research is done on all levels - experimental, theoretical, and numerical. This thesis presents a numerical simulation approach based on solving partial differential equations from the continuum mechanics framework. The results obtained can be used to predict the dynamics and thermodynamics of the system or serve as input data for stochastic simulations. Using this approach, it is also possible to simulate actual laboratory experiments numerically. 1
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Active Brownian Ratchets
Kolář, Martin ; Holubec, Viktor (advisor) ; Novotný, Tomáš (referee)
A currently intensively researched area of physics is Active Brownian ratchets, devi- ces capable of directing the motion of particles by utilizing their activity. In the bachelor thesis, we proposed a ratchet operating only due to the spatial dependence of the par- ticle velocity, and thus without the use of periodic potentials or walls. We verified its functionality using two mutually independent numerical methods. Our main result is the dependence of the particle probability flux on parameters describing the relative influ- ence of activity and diffusion on particle motion. Using the mean value of the particle orientation, we have illustrated its behaviour in the ratchet. This allowed us to reveal how the ratchet works. 1
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Nonequilibrium Thermodynamics of Small Systems
Holubec, Viktor
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...
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Quantum thermodynamics
Sedlák, Oldřich ; Holubec, Viktor (advisor) ; Chvosta, Petr (referee)
Quantum coherence is being viewed as a possible resource that could improve the performance of quantum technologies. This thesis analyzes a quantum heat engine model inspired by Dorfman et al. (PNAS vol. 110 no. 8) while using a standard Markovian quantum optical master equation in the Lindblad form. Steady-state coherence arises from the degeneracy of the two upper energy levels and its effects become significant for near-perfect alignment of the associated transition dipole moments. For the maximum alignment, the steady-state cur- rent becomes highly dependent on the relative phase and exhibits quantum in- terference. The performed numerical calculations show some promise of possible enhancement of the current above the classical limit. 1
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Carnot efficiency revisited
Klimovič, Filip ; Holubec, Viktor (advisor) ; Ryabov, Artem (referee)
We introduce a simple discrete model of a molecular heat engine. The engine's dynamics is strongly influenced by thermal motion of ambient molecules. Thermodynamic quantities of heat and work observed at mesoscopic scale are thus fluctuating. We focus on the efficiency of the engine, which fluctuates as well. We use analytic methods as well as Monte Carlo simulations in order to examine probability distribution of quantities mentioned above. Exact analytic solution is found in case of short trajectories, while large deviation theory is exploited for long ones. Our interest in the efficiencies' definition is no less than in its values. Properties of the large deviation function stated in literature are demonstrated within the results. Meanwhile we show an example of an engine, where the properties regarded as general are not applied. Powered by TCPDF (www.tcpdf.org)
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Study of the relaxation into a stochastic limit cycle
Hrubovský, Martin ; Holubec, Viktor (advisor) ; Šomvársky, Ján (referee)
We consider a microscopic two-level system in contact with a heat reservoir. We assume a time-periodic difference between the energies of the two levels. The system dynamics is assumed to be Markovian. From the correspond- ing master equation we calculate the dynamics of such a system in the form of a propagator matrix. Under the assumption of the detailed balance we further calculate the limit cycle probability distribution (which the system will attain after a long time) as an eigenvector of the propagator. We also find a transcen- dental equation for the initial condition that minimizes the entropy production over the first driving period. These two distributions are then expanded in an irreversibility parameter and compared. We discover that up to the first term in the irreversibility parameter (for a slow driving), the Boltzmann equilibrium probability distribution is the average of the limit cycle and entropy minimizing distribution. 1
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Theoretical description of unequilibrium energy transformation processes on the level of molecular structures
Holubec, Viktor ; Chvosta, Petr (advisor) ; Netočný, Karel (referee) ; Maass, Philipp (referee)
Title: Theoretical description of unequilibrium energy transformation processes on the level of molecular structures Author: Viktor Holubec Department: Department of Macromolecular Physics Supervisor: prof. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: The thesis is devoted to the thermodynamics of externally driven mesoscopic sys- tems. These systems are so small that the thermodynamic limit ceases to hold and the probabilistic character of the second law cannot be ignored. Thermal forces becomes comparable to other forces acting on the system and they have to be incorporated in the underlying dynamical law, i.e., in the master equation for discrete systems, and in the Fokker-Planck equation for continuous ones. In the first part of the thesis we investigate dynamics and energetics of mesoscopic systems during non-equilibrium isothermal processes. Due to the stochastic na- ture of the dynamics, the work done on the system by the external forces must be treated as a random variable. We derive an exact analytical form of the work probability density for several model systems. In particular, the knowledge of the exact formula improves the analysis of experimental data using the recent- ly discovered fluctuation theorems. In the second part of the thesis we study a non-equilibrium...
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Nonequilibrium Thermodynamics of Small Systems
Holubec, Viktor
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...
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