Hmm, I don't know enough to give you a confident answer yet. The provided extracts do not contain specific information about auto-logout functionality due to inactivity in Ory Hydra or Ory Kratos. However, they do provide extensive details on how to implement logout functionality in general. For Ory Kratos, you can implement user logout in server-rendered browser applications, single page applications (SPA), and native API applications. The logout flow is used to terminate an Ory Identities session. You can find more details in the [Ory Kratos documentation](https://www.ory.sh/docs/kratos/self-service/flows/user-logout). For Ory Hydra, you can implement your own logout endpoint using the Ory SDK. This includes handling both back-channel and front-channel logout requests. More information can be found in the [Ory Hydra documentation](https://www.ory.sh/docs/hydra/guides/logout). For more specific information about auto-logout due to inactivity, I would recommend checking the official Ory documentation or reaching out to the Ory community for further assistance.