How do we understand the dynamics and nonequilibrium? In our physics classes,we have learned lots of laws to describe the motion of particles,such as Newton's second Law

$$F = m \ddot x$$

in classical mechanics,and also the famous Schrödinger equation

$$i\hbar~\partial_t|\Psi\rangle  = H|\Psi\rangle$$

in quantum mechanics.These laws are important and powerful to predict the development of one or two particles,especially we can follow exactly the time-evolution if we know the initial conditions.But,the most important thing we care is of course the dynamics for our system or particles.
So my first question is :

$$\textbf{dynamics process = nonequilibrium process ?}$$


The concept of $\textbf{Nonequilibrium}$ seems only appear in the context of statistical mechanics,in which we talk about so much the $\textbf{thermal}$ equilibrium properties for our physical system and naively drop the important time variable.So my second question is can we construct a Newton-like or Schrödinger-like equation of motion to describe the thermal nonequilibrium for many particles? Or more generally are there some more profound 

$$\textbf{relations between the thermal
 nonequilibrium and mechanical nonequilibrium ?}$$

in which we always believe the quantum particles always live in mechanical nonequilibrium due to uncertainty principle.

 A: 
So my first question is: dynamics = non-equilibrium?

Dynamics refers to the time evolution of a system under the effect of some field or force. Supposing you are equipped with a correct physical theory (whether it be probabilistic or deterministic), it is not guaranteed that you will be able to produce a meaningful prediction. Often times, systems are too complex and one can actually prove that the dynamics cannot be expressed as an analytic equation (ie- you must use a computer to make predictions). In some cases, even an analytic solution won't do you much good: in some systems, one would have to know the initial conditions of the system with extreme (perhaps impossible!) precision in order to make meaningful predictions (see Chaos Theory).
Often times we are interested in systems where there not one, two or three particles, but $10^{25}$ particles (eg - the number of molecules in a glass of water). In such systems, there is no hope for an analytical solution and it is not possible to observe the initial positions and velocities of all the particles. It is in these extreme cases that Statistical Mechanics and Thermal Physics thrive. Rather than solve for the dynamics of the microscopic system, we can measure and predict macroscopic quantities like temperature, phase of matter, electrical conductivity, thermal conductivity, etc. 
These macroscopic quantities however are rarely defined if the system is not in equilibrium. In such cases we say that a system is a non-equilibrium system. Examples of non-equilibrium systems include a gas expanding into a vacuum (think of an astronaut opening an air hatch) or a living human being (you're only at equilibrium with you environment when you are dead).

Can we construct a Newton-like or Schrödinger-like equation of motion for a system of many particles?

There are currently no general theories about how non-equilibrium systems evolve but there are several useful approximations. Of primary importance is the fluctuation-dissipation theorem which details how a system near equilibrium responds to small fluctuations/applied forces. Other great advances include Jarzynski's equality and Crook's Fluctuation Theorem.

And my final question is due to many kinds of correlation or interaction between particles, the macroscopic physical system composed by many particles, never can keep in peace, namely they will be dynamical forever?

I suppose you mean dynamical system to mean a system whose components are always moving relative to each other. A system of many particles can comes to rest ("peace"). Given certain initial conditions, one could imagine an enormous number of particles collapsing together under the force of gravity to form one sedentary aggregate.
A: Since quantum mechanical effects are only significant for "small" objects, the question of how to extend a QM-like equation of motion to a system of "many" particles doesn't have much practical importance, except in very special circumstances (e.g. at temperatures very close to absolute zero).
At the non-quantum scale, one approach is to ignore the individual particles and assume a continuous distribution of matter. This approach is known as Continuum Mechanics. 
Continuum mechanics naturally splits into Solid Mechanics  and Fluid Mechanics, since the macroscopic behaviour of solids and fluids is fundamentally different - the "particles" in a solid that are "close to each other" at one instant in time tend to stay that way for all other times, but that is not true for fluids.
In general, solid and fluid mechanics considers the behaviour of flexible continuous bodies, though a first course in "classical mechanics" usually only deals with rigid continuous bodies (and therefore considers only solids, and not fluids) where a rigid body is modelled as collection of point particles whose relative position in space is fixed.
For many purposes one can ignore the dynamic behaviour of the individual particles, and include the macroscopic effects of it by things like temperature-dependent material properties for solids and liquids, the internal energy of a gas as modeled by the ideal gas laws, etc.
