In this paper, we summarize some recent advances related to the energetic variational
approach (EnVarA), a general variational framework of building thermodynamically …

Motivated by the occurrence in rate functions of time-dependent large-deviation principles,
we study a class of non-negative functions ℒ that induce a flow, given by ℒ (ρ t, ρ ̇ t)= 0 …

Existing computational methods that use single-cell RNA-sequencing (scRNA-seq) for cell
fate prediction do not model how cells evolve stochastically and in physical time, nor can …

We estimate stochastic processes that govern the dynamics of evolving populations such as
cell differentiation. The problem is challenging since longitudinal trajectory measurements of …

We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …

We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …

Abstract Onsager's 1931 “reciprocity relations” result connects microscopic time reversibility
with a symmetry property of corresponding macroscopic evolution equations. Among the …

Classical gradient systems have a linear relation between rates and driving forces. In
generalized gradient systems we allow for arbitrary relations derived from general non …

In this paper we discuss the connections between a Vlasov–Fokker–Planck equation and an
underlying microscopic particle system, and we interpret those connections in the context of …

We present a structure-preserving Eulerian algorithm for solving-gradient flows and a
structure-preserving Lagrangian algorithm for solving generalized diffusions. Both …