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.Comment: 178 pages, 19 figures, 2 tables, PHD thesis; defended in October 2013
at Faculty of Mathematics and Physics at Charles University in Pragu