  In recent years, the unified theory of information and thermodynamics has
been intensively discussed in the context of stochastic thermodynamics. The
unified theory reveals that information theory would be useful to understand
non-stationary dynamics of systems far from equilibrium. In this letter, we
have found a new link between stochastic thermodynamics and information theory
well known as information geometry. By applying this link, an information
geometric inequality can be interpreted as a thermodynamic uncertainty
relationship between speed and thermodynamic cost. We have numerically applied
an information geometric inequality to a thermodynamic model of biochemical
enzyme reaction.
