We study the asymmetric brownian energy, a model of heat conduction defined on the one-
dimensional finite lattice with open boundaries. The system is shown to be dual to the …

We show that a coalescence equation exhibits a variety of critical behaviors, depending on
the initial condition. This equation was introduced a few years ago to understand a toy …

In this paper, a generalized version of dynamic asymmetric simple exclusion process
(ASEP) is introduced, and it is shown that the process has a Markov duality property with the …

We point out that the mean-field theory of avalanches in the dynamics of elastic interfaces,
the so-called Brownian force model (BFM) developed recently in non-equilibrium statistical …

Stochastic differential equations are widely used in various fields; in particular, the
usefulness of duality relations has been demonstrated in some models such as population …

The Koopman operator is beneficial for analyzing nonlinear and stochastic dynamics; it is
linear but infinite-dimensional, and it governs the evolution of observables. The extended …