  In this paper, we propose a new measure for the freshness of information,
which uses the mutual information between the real-time source value and the
delivered samples at the receiver to quantify the freshness of the information
contained in the delivered samples. Hence, the "aging" of the received
information can be interpreted as a procedure that the above mutual information
reduces as the age grows. In addition, we consider a sampling problem, where
samples of a Markov source are taken and sent through a queue to the receiver.
In order to optimize the freshness of information, we study the optimal
sampling policy that maximizes the time-average expected mutual information. We
prove that the optimal sampling policy is a threshold policy and find the
optimal threshold exactly. Specifically, a new sample is taken once a
conditional mutual information term reduces to a threshold, and the threshold
is equal to the optimum value of the time-average expected mutual information
that is being maximized. Numerical results are provided to compare different
sampling policies.
