  We study thermodynamic operations which bring a nonequilibrium steady state
(NESS) to another NESS in physical systems under nonequilibrium conditions. We
model the system by a suitable Markov jump process, and treat thermodynamic
operations as protocols according to which the external agent varies parameters
of the Markov process. Then we prove, among other relations, a NESS version of
the Jarzynski equality and the extended Clausius relation. The latter can be a
starting point of thermodynamics for NESS. We also find that the corresponding
nonequilibrium entropy has a microscopic representation in terms of symmetrized
Shannon entropy in systems where the microscopic description of states involves
"momenta". All the results in the present paper are mathematically rigorous.
