Stochastic thermodynamics as reviewed here systematically provides a
framework for extending the notions of classical thermodynamics like work, heat
and entropy production to the level of individual trajectories of well-defined
non-equilibrium ensembles. It applies whenever a non-equilibrium process is
still coupled to one (or several) heat bath(s) of constant temperature.
Paradigmatic systems are single colloidal particles in time-dependent laser
traps, polymers in external flow, enzymes and molecular motors in single
molecule assays, small biochemical networks and thermoelectric devices
involving single electron transport. For such systems, a first-law like energy
balance can be identified along fluctuating trajectories. Various integral and
detailed fluctuation theorems, which are derived here in a unifying approach
from one master theorem, constrain the probability distributions for work, heat
and entropy production depending on the nature of the system and the choice of
non-equilibrium conditions. For non-equilibrium steady states, particularly
strong results hold like a generalized fluctuation-dissipation theorem
involving entropy production. Ramifications and applications of these concepts
include optimal driving between specified states in finite time, the role of
measurement-based feedback processes and the relation between dissipation and
irreversibility. Efficiency and, in particular, efficiency at maximum power,
can be discussed systematically beyond the linear response regime for two
classes of molecular machines, isothermal ones like molecular motors, and heat
engines like thermoelectric devices, using a common framework based on a cycle
decomposition of entropy production.

随机热力学是将经典热力学的概念（如功、热以及熵的产生）扩展到非平衡集合的个体轨迹的框架，主要应用于单胶体颗粒、聚合物、酶和分子电机、小型生化网络以及热电器件等系统中，各种波动定理限制着功、热和熵产生的概率分布，并可以通过一个主定理来规定。