Stability and causality of Carter’s multifluid theory
Lorenzo Gavassino
Abstract
Abstract Stability and causality are studied for linear perturbations about equilibrium in Carter’s multifluid theory. Our stability analysis is grounded on the requirement that the entropy of the multifluid, plus that of the environment, must be maximised at equilibrium. This allows us to compute a quadratic Lyapunov functional, whose positive definiteness implies stability. Furthermore, we verify explicitly that, also for multifluids, thermodynamic stability implies linear causality. As a notable stability condition, we find that the entrainment matrix must always be positive definite, confirming a widespread intuition.
Topics & Concepts
Positive definitenessPhysicsCausality (physics)Positive-definite matrixStability (learning theory)Quadratic equationClassical mechanicsApplied mathematicsStatistical physicsMathematical economicsMathematicsQuantum mechanicsEigenvalues and eigenvectorsComputer scienceMachine learningGeometryAdvanced Thermodynamics and Statistical MechanicsCosmology and Gravitation TheoriesQuantum Electrodynamics and Casimir Effect