Related papers: Onsager's variational principle for nonreciprocal …
This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
When time reversal is broken the viscosity tensor can have a non vanishing odd part. In two dimensions, and only then, such odd viscosity is compatible with isotropy. Elementary and basic features of odd viscosity are examined by…
Non-reciprocal interactions in elastic media give rise to rich non-equilibrium behaviors, but controllable experimental realizations of such odd elastic phenomena remain scarce. Building on recent breakthroughs in electrical analogs of…
An overview is given of recent advances in the nonequilibrium statistical mechanics of quantum systems and, especially, of time-reversal symmetry relations that have been discovered in this context. The systems considered are driven out of…
Motility is a fundamental feature of living matter, encompassing single cells and collective behavior. Such living systems are characterized by non-conservativity of energy and a large diversity of spatio-temporal patterns. Thus,…
We discuss the linear hydrodynamic response of a two-dimensional active chiral compressible fluid with odd viscosity. The viscosity coefficient represents broken time-reversal and parity symmetries in the 2D fluid and characterizes the…
The non-standard Lagrangians (NSLs) for dissipative-like dynamical systems were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of…
We construct solutions to the three-dimensional Euler equations exhibiting anomalous dissipation in finite time through a vanishing viscosity limit. Inspired by \cite{BDL23} and \cite{cheskidov2023dissipation}, we extend the…
We study the rheological signatures of departure from equilibrium in two-dimensional viscous fluids with and without internal spin. Under the assumption of isotropy, we provide the most general linear constitutive relations for stress and…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the…
A discrete theory for implicit nonholonomic Lagrangian systems undergoing elastic collisions is developed. It is based on the discrete Lagrange-d'Alembert-Pontryagin variational principle and the dynamical equations thus obtained are the…
We use the Schwinger action principle to obtain the equations of motion in the Koopman-von Neumann operational version of classical mechanics. We restrict our analysis to non-dissipative systems. We show that the Schwinger action principle…
Continuum-type constitutive relations of odd matter need to be formulated according to the second law of thermodynamics. Based on the primitive thermodynamics of Edelen, a procedure admitting most general relations, is outlined for…
A fluid, with broken time-reversal symmetry, would exhibit odd transport coefficients, such as odd viscosity, thermal conductivity and diffusion coefficient, which may fundamentally alter the fluid properties and significantly influence the…