## Abstract

We consider a dynamical system with state space M, a smooth, compact subset of some ℝ^{n}, and evolution given by T_{t}, x_{t} = T_{t}x, x ∈ M; T_{t} is invertible and the time t may be discrete, t ∈ ℤ, T_{t} = T^{t}, or continuous, t ∈ ℝ. Here we show that starting with a continuous positive initial probability density ρ(x,0) > 0, with respect to dx, the smooth volume measure induced on M by Lebesgue measure on ℝ^{n}, the expectation value of logρ(x,t), with respect to any stationary (i.e., time invariant) measure v(dx), is linear in t, v(logρ(x,t)) = v(logρ(x,0)) + Kt. K depends only on v and vanishes when v is absolutely continuous with respect to dx.

Original language | English (US) |
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Pages (from-to) | 393-395 |

Number of pages | 3 |

Journal | Chaos |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1998 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics