Finite-time thermodynamic uncertainty relation do not hold for discrete-time Markov process

Understand

Discrete-time counterpart of thermodynamic uncertainty relation (conjectured in P.

• Pietzonka, et.al., arXiv:1702.07699 (2017)) with finite time interval is considered.
• We show that this relation do not hold by constructing a concrete counterexample to this.
• Our finding suggests that the proof of thermodynamic uncertainty relation with finite time interval, if true, should strongly rely on the fact that the time is continuous.