  We report an experimental study of recently formulated entropic Leggett-Garg
inequality (ELGI) by Usha Devi et al. (arXiv: 1208.4491v2 (2012)). This
inequality places a bound on the statistical measurement outcomes of dynamical
observables describing a macrorealistic system. Such a bound is not necessarily
obeyed by quantum systems, and therefore provides an important way to
distinguish quantumness from classical behavior. Here we study ELGI using a
two-qubit nuclear magnetic resonance system. To perform the noninvasive
measurements required for the ELGI study, we prepare the system qubit in a
maximally mixed state as well as use the `ideal negative result measurement'
procedure with the help of an ancilla qubit. The experimental results show a
clear violation of ELGI by over four standard deviations. These results agree
with the predictions of quantum theory. The violation of ELGI is attributed to
the fact that certain joint probabilities are not legitimate in the quantum
scenario, in the sense they do not reproduce all the marginal probabilities.
Using a three-qubit system, we experimentally demonstrate that three-time joint
probabilities do not reproduce certain two-time marginal probabilities.
