Stochastic thermodynamics provides a framework for
describing small systems embedded in a heat bath and
externally driven to non-equilibrium. Examples are colloidal
particles in time-dependent optical traps, single
biomolecules manipulated by optical tweezers or AFM tips,
and motor proteins driven by ATP excess. A first-law like
energy balance allows to identify applied work and
dissipated heat on the level of a single stochastic
trajectory. Total entropy production includes not only this
heat but also changes in entropy associated with the state
of the small system. Within such a framework, exact results
like an integral fluctuation theorem for total entropy
production valid for any initial state, any time-dependent
driving and any length of trajectories can be proven .
These theoretical predictions have been illustrated and
tested with experiments on a colloidal particle pushed by a
periodically modulated laser towards a surface . Key
elements of this framework like a stochastic entropy can
also be applied to athermal systems as experiments on an
optically driven defect center in diamond show [3,4]. For
mechanically driven non-equilibrium steady states, the
violation of the fluctuation-dissipation theorem can be
quantified as an additive term directly related to broken
detailed balance (rather than a multiplicative effective
temperature) [5,6]. Integrated over time, a generalized
Einstein relation appears which we have recently verified
experimentally . Finally, optimal protocols are derived
which (i) minimize the work required to switch from one
equilibrium state to another in finite time  and (ii)
maximize the power of stochastic heat engines operating
between two heat baths .
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