  This PhD thesis deals with the Markov picture of developed turbulence from
the theoretical point of view. The thesis consists of two parts. The first part
introduces stochastic thermodynamics, the second part aims at transferring the
concepts of stochastic thermodynamics to developed turbulence. / Central in
stochastic thermodynamics are Markov processes. An elementary example is
Brownian motion. In contrast to macroscopic thermodynamics, the work done and
the entropy produced for single trajectories of the Brownian particles are
random quantities. Statistical properties of such fluctuating quantities are
central in the field of stochastic thermodynamics. Prominent results are
so-called fluctuation theorems which express the balance between production and
consumption of entropy and generalise the second law. / Turbulent cascades of
eddies are assumed to be the predominant mechanism of turbulence generation and
fix the statistical properties of developed turbulent flows. An intriguing
phenomenon of developed turbulence, known as small-scale intermittency, are
violent small-scale fluctuations in flow velocity that exceed any Gaussian
prediction. / In analogy to Brownian motion, it is demonstrated in the thesis
how the assumption of the Markov property leads to a Markov process for the
turbulent cascade that is equivalent to the seminal K62 model. In addition to
the K62 model, it is demonstrated how many other models of turbulence can be
written as a Markov process, including scaling laws, multiplicative cascades,
multifractal models and field-theoretic approaches. Based on the various Markov
processes, the production of entropy along the cascade and the corresponding
fluctuation theorems is discussed. In particular, experimental data indicates
that entropy consumption is linked to small-scale intermittency, and a
connection between entropy consumption and an inverse cascade is suggestive.
