Loss of physical reversibility in reversible systems

Amir Sagiv*, Adi Ditkowski, Roy H. Goodman, Gadi Fibich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have a time-reversal symmetry, such as the Nonlinear Schrödinger equation and the ϕ4 equation can become ”physically irreversible”. By this, we mean that realistically-small experimental errors in measuring the output can lead to dramatic differences between the recovered input and the original one. The loss of reversibility reveals a natural ”arrow of time”, reminiscent of the thermodynamic one, which is the direction in which the radiation is emitted outward. Our results are relevant to imaging and reversal applications in nonlinear optics.

Original languageEnglish
Article number132515
JournalPhysica D: Nonlinear Phenomena
StatePublished - Sep 2020


FundersFunder number
Israel Science Foundation177/13
Israel Science Foundation


    • Nonlinear Schrödinger
    • Nonlinear dynamics
    • Reversibility
    • Stability
    • ϕ equation


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