{
  "id": "1709.05968",
  "version": "v1",
  "published": "2017-09-15T06:49:14.000Z",
  "updated": "2017-09-15T06:49:14.000Z",
  "title": "Thermodynamics and stability of non-equilibrium steady states in open systems",
  "authors": [
    "Miroslav Bulíček",
    "Josef Málek",
    "Vít Průša"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems. Unfortunately, the limitation to thermodynamically isolated systems is essential, and the standard arguments are not applicable even for some very simple thermodynamically open systems. On the other hand, the nonlinear stability of inhomogenous non-equilibrium states in thermodynamically open systems is usually investigated using the so-called energy method. However, when the method is used in the stability analysis of coupled thermomechanical systems, the designation energy method is clearly a misnomer. The reason is that one of the key quantities of interest is the volume integral of the square of temperature field, which is by no means linked to the energy in the physical sense of the word. This indicates that the mathematical method is used rather artificially without a tight link to the physics. Consequently, it seems that thermodynamical concepts are of no use in the nonlinear stability analysis of thermodynamically open systems. We show that this is not true. In particular, we propose a construction that in the case of simple heat conduction problem leads to a physically well motivated Lyapunov functional, which effectively replaces the artificial Lyapunov functional used in the standard energy method. The proposed construction seems to be generic enough to be applied in more complex thermomechanical settings, hence it could provide a tool for nonlinear stability analysis of thermodynamically open systems that are currently beyond the reach of the standard energy method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-15T06:49:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q79",
      "37L15",
      "37B25"
    ],
    "keywords": [
      "non-equilibrium steady states",
      "thermodynamically open systems",
      "nonlinear stability analysis",
      "homogeneous equilibrium steady states",
      "standard energy method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}