Various experimental techniques have been advanced in recent
years to measure non-equilibrium energy transformations on
themicroscopic scale of single molecules. In general, the systems
studied inthe correspondingexperiments are exposed to strong
thermal fluctuations and thus the relevant energetic variables such
as work and heat become stochastic.
This thesis addresses challenging theoretical problems in this
active field of current research: 1) Exact analytical solutions of
work and heat distributions for isothermal non-equilibrium
processes in suitable models are obtained; 2) Corresponding
solutions for cyclic processes involving two different heat
reservoirs are found; 3) Optimization of periodic driving protocols
for such cyclic processes with respect to maximal output power,
efficiency and minimal power fluctuations is studied.
The exact solutions for work and heat distributionsprovide
areference for theoretical investigations of more complicated
models, giving insight into the structure of the tail of work
distributions andserving asvaluable test cases for simulations of
the underlying stochastic processes."
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