A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

Thermodynamics serves as a universal means for studying physical systems from an energy
perspective. In recent years, with the establishment of the field of stochastic and quantum …

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 …

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 …

The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative
fluctuation of observables and thermodynamic quantities such as dissipation and dynamical …

We study a relationship between optimal transport theory and stochastic thermodynamics for
the Fokker-Planck equation. We show that the lower bound on the entropy production is the …

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

The relationship between the thermodynamic and computational properties of physical
systems has been a major theoretical interest since at least the 19th century. It has also …

We derive a variational expression for the correlation time of physical observables in steady-
state diffusive systems. As a consequence of this variational expression, we obtain lower …

Understanding current fluctuations is of fundamental importance and paves the way for the
development of practical applications. According to the thermodynamic and kinetic …