Complementary relations in non-equilibrium stochastic processes

Eun Jin Kim, S. B. Nicholson

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We present novel complementary relations in non-equilibrium stochastic processes. Specifically, by utilising path integral formulation, we derive statistical measures (entropy, information, and work) and investigate their dependence on variables (x, v), reference frames, and time. In particular, we show that the equilibrium state maximises the simultaneous information quantified by the product of the Fisher information based on x and v while minimising the simultaneous disorder/uncertainty quantified by the sum of the entropy based on x and v as well as by the product of the variances of the PDFs of x and v. We also elucidate the difference between Eulerian and Lagrangian entropy. Our theory naturally leads to Hamilton-Jacobi relation for forced-dissipative systems.

Original languageEnglish
Pages (from-to)1613-1618
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number28-29
Early online date22 Apr 2015
Publication statusPublished - 28 Aug 2015
Externally publishedYes


  • Chaos
  • Entropy
  • Information
  • Non-equilibrium
  • Stochastic process

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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