相关论文: A variational principle for computing nonequilibri…
We derive the dual variational principle (principle of minimal complementary energy) for the nonlocal nonlinear scalar diffusion problem, which may be viewed as the nonlocal version of the $p$-Laplacian operator. We establish existence and…
A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the…
In this article the Gordan theorem is applied to the thermodynamics of a chemical reaction network at steady state. From a theoretical viewpoint it is equivalent to the Clausius formulation of the second law for the out of equilibrium…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
The field-dependent equilibrium thermodynamics is derived with two methods: either by using the potential formalism either by the statistical method. Therefore, Pontrjagin's extremum principle of control theory is applied to an extended…
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…
Optimality principles in nonequilibrium transport networks are linked to a thermodynamic formalism based on generalized transport potentials endowed with Legendre duality and related contact structure. This allows quantifying the distance…
The discrimination of quantum processes, including quantum states, channels, and superchannels, is a fundamental topic in quantum information theory. It is often of interest to analyze the optimal performance that can be achieved when…
A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…
Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at…
We obtain the variational equations for backward stochastic differential equations in recursive stochastic optimal control problems, and then get the maximum principle which is novel. The control domain need not be convex, and the generator…
We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. We show that in the case when the flow is a monotonically…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
In this paper, the problem of finding optimal success probabilities of static linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of…
A systematic approach to finding variational approximation in an otherwise intractable non-conjugate model is to exploit the general principle of convex duality by minorizing the marginal likelihood that renders the problem tractable. While…
There exists in nature many examples of systems presenting self-limiting behaviour: population dynamics, structure engineering, Townsend's electron breakdown, nuclear decay in radioactive equilibrium, histeresis process, meteorological…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…