### Abstract

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 language | English |
---|---|

Pages (from-to) | 1613-1618 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 379 |

Issue number | 28-29 |

Early online date | 22 Apr 2015 |

DOIs | |

Publication status | Published - 28 Aug 2015 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Complementary relations in non-equilibrium stochastic processes'. Together they form a unique fingerprint.

## Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*379*(28-29), 1613-1618. https://doi.org/10.1016/j.physleta.2015.04.031