We review various bounds concerning out-of-equilibrium dynamics in few-level and many-
body quantum systems. We primarily focus on closed quantum systems but will also mention …

Many biological functions are executed by molecular machines, which like man-made
motors are powered by chemical energy, released by adenosine triphosphate hydrolysis …

Thermodynamic uncertainty relations yield a lower bound on entropy production in terms of
the mean and fluctuations of a current. We derive their general form for systems under …

We investigate the connection between the time evolution of averages of stochastic
quantities and the Fisher information and its induced statistical length. As a consequence of …

Thermodynamic uncertainty relations (TURs) are the inequalities which give lower bounds
on the entropy production rate using only the mean and the variance of fluctuating currents …

We extend a class of recently derived thermodynamic uncertainty relations to vector-valued
observables. In contrast to the scalar-valued observables examined previously, this …

According to the laws of thermodynamics, no heat engine can beat the efficiency of a Carnot
cycle. This efficiency traditionally comes with vanishing power output and practical designs …

We discuss how to use correlations between different physical observables to improve
recently obtained thermodynamics bounds, notably the fluctuation-response inequality and …

We show that the entropy production rate bounds the rate at which physical processes can
be performed in stochastic systems far from equilibrium. In particular, we prove the …

For periodically driven systems, we derive a family of inequalities that relate entropy
production with experimentally accessible data for the mean, its dependence on driving …