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Energetics of diffusion in time-dependent parabolic potential.
Škvára, Jan ; Chvosta, Petr (advisor) ; Netočný, Karel (referee)
In this thesis we are going to study the dynamics and energetics of the dif- fusion of a Brownian particle in a time-dependent parabolic potential. Our central quantity is a random variable corresponding to the work done on the particle due to the time dependency of the potential. We present new exact analytical ex- pression for the probability density function for the work variable in a situation, where the potential is piecewise constant in the time variable. Furthermore, this result is used to develop a hierarchy of approximations which yield the density function for an arbitrary time-dependent parabolic potential. 1
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Stochastic dynamics and energetics of biomolecular systems
Ryabov, Artem ; Chvosta, Petr (advisor) ; Novotný, Tomáš (referee) ; Papáček, Štěpán (referee)
Title: Stochastic dynamics and energetics of biomolecular systems Author: Artem Ryabov Department: Department of Macromolecular Physics Supervisor: prof. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: The thesis comprises exactly solvable models from non-equilibrium statistical physics. First, we focus on a single-file diffusion, the diffusion of particles in narrow channel where particles cannot pass each other. After a brief review, we discuss open single-file systems with absorbing boundaries. Emphasis is put on an interplay of absorption process at the boundaries and inter-particle entropic repulsion and how these two aspects affect the dynam- ics of a given tagged particle. A starting point of the discussions is the exact distribution for the particle displacement derived by order-statistics argu- ments. The second part of the thesis is devoted to stochastic thermodynam- ics. In particular, we present an exactly solvable model, which describes a Brownian particle diffusing in a time-dependent anharmonic potential. The potential has a harmonic component with a time-dependent force constant and a time-independent repulsive logarithmic barrier at the origin. For a particular choice of the driving protocol, the exact work characteristic func- tion is obtained. An asymptotic analysis of...
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Energetics of diffusion in time-dependent parabolic potential.
Škvára, Jan ; Chvosta, Petr (advisor) ; Netočný, Karel (referee)
In this thesis we are going to study the dynamics and energetics of the dif- fusion of a Brownian particle in a time-dependent parabolic potential. Our central quantity is a random variable corresponding to the work done on the particle due to the time dependency of the potential. We present new exact analytical ex- pression for the probability density function for the work variable in a situation, where the potential is piecewise constant in the time variable. Furthermore, this result is used to develop a hierarchy of approximations which yield the density function for an arbitrary time-dependent parabolic potential. 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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Thermodynamics of interacting brownian particles
Herčík, Michal ; Chvosta, Petr (advisor) ; Ryabov, Artem (referee)
The thesis comprises single-file diffusion in an external time-dependent potential, the diffusion of particles in narrow channel where particles can not pass each other. We discuss the role of order statistics solving the dynamics of the particles. We focus on application of perturbation theory on Fokker- Planck equation for the combined stochastic process of position and work. The calculation of the first and second moment of work for a set of particles analytically. The comparison of these results with results based on computer simulations of trajectories. Computer simulation of marginal PDF of work for left and right particle and simultaneous PDF for a set of two external driven particles. 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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Stochastic dynamics and energetics of biomolecular systems
Ryabov, Artem ; Chvosta, Petr (advisor) ; Novotný, Tomáš (referee) ; Papáček, Štěpán (referee)
Title: Stochastic dynamics and energetics of biomolecular systems Author: Artem Ryabov Department: Department of Macromolecular Physics Supervisor: prof. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: The thesis comprises exactly solvable models from non-equilibrium statistical physics. First, we focus on a single-file diffusion, the diffusion of particles in narrow channel where particles cannot pass each other. After a brief review, we discuss open single-file systems with absorbing boundaries. Emphasis is put on an interplay of absorption process at the boundaries and inter-particle entropic repulsion and how these two aspects affect the dynam- ics of a given tagged particle. A starting point of the discussions is the exact distribution for the particle displacement derived by order-statistics argu- ments. The second part of the thesis is devoted to stochastic thermodynam- ics. In particular, we present an exactly solvable model, which describes a Brownian particle diffusing in a time-dependent anharmonic potential. The potential has a harmonic component with a time-dependent force constant and a time-independent repulsive logarithmic barrier at the origin. For a particular choice of the driving protocol, the exact work characteristic func- tion is obtained. An asymptotic analysis of...
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Heat processes in non-equilibrium stochastic systems
Pešek, Jiří ; Netočný, Karel (advisor) ; Speck, Thomas (referee) ; Lisý, Vladimír (referee)
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the quasistatic limit for a large class of non-equilibrium models. As an application of general methods a natural non-equilibrium generalization of heat capacity is introduced and its properties are analyzed in detail, including an anomalous far-from-equilibrium behavior. The developed methods are further applied to the related problem of time-scale separation where they enable to describe the effective dynamics of both slow and fast degrees of freedom in a more precise way. Powered by TCPDF (www.tcpdf.org)
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