System/environment duality of nonequilibrium observables

On networks representing probability currents between states of a system, we generalize Schnakenberg's theory of nonequilibrium observables to nonsteady states, with the introduction of a new set of macroscopic observables that, for planar graphs, are related by a duality. We apply this duality to the linear regime, obtaining a dual proposition for the minimum entropy production principle, and to discrete electromagnetism, finding that it exchanges fields with sources. We interpret duality as reversing the role of system and environment, and discuss generalization to nonplanar graphs. The results are based on two theorems regarding the representation of bilinear and quadratic forms over the edge vector space of an oriented graph in terms of observables associated to cycles and cocycles.

• Publication year

  2011

• Venue

  arXiv: Statistical Mechanics

• Publication date

  2011-06-07

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1007/978-3-319-16619-3_13arXiv 1106.1280
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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