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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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Contour methods in the mathematical theory of phase transitions
Nagy, Oliver ; Zahradník, Miloš (advisor) ; Netočný, Karel (referee)
Title: Contour methods in the mathematical theory of phase transitions Author: Oliver Nagy Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Miloš Zahradník, CSc., Department of Mathematical Analysis Abstract: This thesis concerns itself with three topics, namely polymer models, Pirogov-Sinai theory and one-dimensional Dyson models. It contains a short introduction into all three topics. The introduction to Pirogov-Sinai theory will serve as a starting point for a future expanded introductory exposition, since such a material is missing in the contemporary literature. Research result of the first chapter is a detailed combinatorial analysis of cluster expansion of hard-core repulsive polymer model based on 'self-avoiding polymer trees', leading to simplification of the structure of summation in the partition function. In the case of Dyson models we suggest an alternative definition of contours for the one-dimensional Dyson model with the exponent of polynomially-decaying interaction p ∈ (1, 2) that is usable for study using Pirogov-Sinai methods. Keywords: Contours, polymers, cluster expansion, Pirogov-Sinai theory, Dyson model;
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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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Anomalous heat response in nonequilibrium stochastic models
Miřátský, Václav ; Netočný, Karel (advisor) ; Ryabov, Artem (referee)
The bachelor thesis deals with heat capacity generalization to systems in non-equilibrium steady states. The non-equilibrium state is kept by contact with many baths and by action of non-potential forces. Evolution of system is understood to be a Markovian process described in the first part of this thesis. After that the concept of reversible heat is presented and heat capacity matrix is introduced. Following chapter deals with the usage of heat capacity matrix for analysation of two-level model in contact with two baths. At the end the built formalism is used for describtion of transport of fermions through a quantum dot. 1
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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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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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