How to identify the equilibrium state and the steady state? 
1.Is there any difference between the equilibrium state and steady state?
2.Can I just understand thermal equilibrium and nonequilibrium state just from whether the Hamiltonian of the system is time-dependent or time-independent?

 A: To show the difference between steady state and equlibrium state, we can use an example from electromagnetism. When we have a conductor in electrostatic field, and all the charges inside are displaced in such a way, that there is no net electric field inside the volume of the conductor, we have equilibrium state. When you take a piece of conductor and connect it to a battery, so that there is constant current flowing inside, that's steady state. The conductor tries to reach the equlibrium, but there is the battery, which constantly disturbs it.
In thermodynamics, when there is no heat transfer, we have thermal equilibrium. When there is a heat transfer, for example through a plate, placed between heat source and sink and the heat flux density is constant in time we have steady state.
A: 1.The concept of the thermal equilibrium state in general physics will be:

The condition of an isolated system in which the macroscopic quantities that specify its properties, such as pressure, temperature, etc, all remain unchanged with time.So you must hold two criteria to judge your system in or out of equilibrium, namely
I.isolated system;
II.all macroscopic quantities to describe your system are time-independent;
However, for the form of steady state, you need the help coming from the surroundings (in this time your system and the surroundings are making up to an open system),in which the surroundings may supply some temperature difference or any other things, so you, of course, cannot talk about the equilibrium state even though the macroscopic quantities to describe your system are all time-independent.

2.The evolution of your system will be governed by your Hamiltonian so if the Hamiltonian is time-dependent, absolutely the quantities to describe your system may time-dependent.
