Dualistic Hessian Structures Among the Thermodynamic Potentials in the k-Thermostatistics

We explore the information geometric structures among the thermodynamic potentials in the k-thermostatistics, which is a generalized thermostatistics based on the k-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the k-escort expectations and the other with the standard expectations. The associated k-generalized metrics are derived and related to the k-generalized fluctuation-response relations among the thermodynamic potentials in the k-thermostatistics.