The sheriff shall receive expenses necessarily incurred in conveying persons to and from the state hospitals and in conveying persons to and from the state prisons or other state institutions, or to other destinations for the purpose of deportation to other states, or in advancing actual traveling expenses to any person committed to a state institution who is permitted to report to an institution without escort, which expenses shall be allowed as provided by Chapter 6 (commencing with Section 4750) of Title 5 of Part 3 of the Penal Code for cases subject to that chapter, and, otherwise, by the Department of General Services and paid by the state.