Conservation Laws shape Dissipation
نویسندگان
چکیده
Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs—, we dene a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. e former is expressed as the dierence between changes caused by time-dependent drivings and a generalized potential dierence. e laer is a sum over the minimal set of ux–force contributions controlling the dissipative ows across the system. When the system is initially prepared at equilibrium (e.g. by turning o drivings and forces), a nite-time detailed uctuation theorem holds for the dierent contributions. Our approach relies on identifying the complete set of conserved quantities and can be viewed as the extension of the theory of generalized Gibbs ensembles to nonequilibrium situations.
منابع مشابه
Structure of Entropy Solutions for Multi{dimensional Scalar Conservation Laws
An entropy solution u of a multi{dimensional scalar conservation law is not necessarily in BV , even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV {function in the sense that the shock location is codimension{one rectiiable. This result highlights the regularizing eeect of genuine non-linearity in a qualitative way; it is based on the loca...
متن کاملHyperbolic Systems of Conservation Laws
Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with "elastic" response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in...
متن کاملValidity of Nonlinear Geometric Optics for Entropy Solutions of Multidimensional Scalar Conservation Laws
Nonlinear geometric optics with various frequencies for entropy solutions only in L∞ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and L–stability. New multidimensional features are recognized, especially including nonlinear propagations of oscilla...
متن کاملHybrid entropy stable HLL-type Riemann solvers for hyperbolic conservation laws
It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of the flux Jacobian is not needed. We demonstrate in the present work that several HLL-type Riemann solvers are provably entropy stable. Further, we provide con...
متن کاملWaves in Systems of Conservation Laws: Large vs Small Scales
Several results about the stability of waves in systems of conservation/balance laws, disseminated in the litterature, obey to a common rule. The linear/spectral stability of the microscopic pattern (the internal structure of the wave) implies the well-posedness of a macroscopic Cauchy problem for an other system of conservation laws. The latter is often obtained by retaining only the conservat...
متن کاملEntropy Stable Approximations of Nonlinear Conservation Laws
A central problem in computational fluid dynamics is the development of the numerical approximations for nonlinear hyperbolic conservation laws and related time-dependent problems governed by additional dissipative and dispersive forcing terms. Entropy stability serves as an essential guideline in the design of new computationally reliable numerical schemes. My dissertation research involves a ...
متن کامل