Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Relaxation to nonequilibrium

Christian Maes, Karel Netočný

Abstract

We describe the structure of evolution equations for the relaxation toward a steady macroscopic nonequilibrium state. The evolution is characterized as the zero-cost flow for a nonequilibrium and nonlinear extension of the Onsager-Machlup action governing macroscopic dynamical fluctuations, thus following the intrinsic connection between macroscopic fluctuations and response. The approach hinges on two main elements: the principle of local detailed balance, which identifies the relevant thermodynamic forces, and the canonical decomposition of the frenesy into a Legendre pair. Notably, it is the time-symmetric component of the Lagrangian, the frenesy, that shapes the structure of the macroscopic evolution for given forcing. The results can be interpreted as a nonequilibrium generalization for relaxation to steady nonequilibrium conditions of the well-established GENERIC formalism, in which relaxation to equilibrium is described by a dissipative gradient flow superimposed on a Hamiltonian flow.

Relaxation to nonequilibrium

Abstract

We describe the structure of evolution equations for the relaxation toward a steady macroscopic nonequilibrium state. The evolution is characterized as the zero-cost flow for a nonequilibrium and nonlinear extension of the Onsager-Machlup action governing macroscopic dynamical fluctuations, thus following the intrinsic connection between macroscopic fluctuations and response. The approach hinges on two main elements: the principle of local detailed balance, which identifies the relevant thermodynamic forces, and the canonical decomposition of the frenesy into a Legendre pair. Notably, it is the time-symmetric component of the Lagrangian, the frenesy, that shapes the structure of the macroscopic evolution for given forcing. The results can be interpreted as a nonequilibrium generalization for relaxation to steady nonequilibrium conditions of the well-established GENERIC formalism, in which relaxation to equilibrium is described by a dissipative gradient flow superimposed on a Hamiltonian flow.
Paper Structure (12 sections, 40 equations)

This paper contains 12 sections, 40 equations.

Table of Contents

  1. Introduction
  2. Main result
  3. Structure of dynamical fluctuations
  4. Structure of relaxation equation
  5. Remarks
  6. General argument
  7. Setup
  8. Canonical structure
  9. Relaxation equation
  10. Constructive aspects
  11. Examples
  12. Conclusion

Theorems & Definitions (2)

  • Example 5.1: Underdamped motion with a rotational force
  • Example 5.2: Driven Vlasov--Fokker-Planck equation