I'm having trouble understanding the quasistatic process concept. I understand that for any process we have well defined initial and final states and the problem is in specifying the path, and the path is important as we need to know it in order to calculate work or heat because they vary depending on the path.
But I don't quite understand how implementing the process slowly can make the system in equilibrium at all points during the process, in other words, how does the system change but in the same time it remains in equilibrium? Also I read in my textbook that if a piston compresses a gas very fast, that results in a higher pressure region near the piston's surface and hence the pressure is not uniform in the gas.
I just find all of that confusing and I want to understand why the concept of quasistatic processes is important and what problem would there be in the theory of thermodynamics if we don't define processes this way? ( we cant apply integration if there is not a set of points or a path for the process?
And if we want a path we have to assume that at any point the pressure(or any property) is uniform and we can only assume that if the process is done extremely slowly so that its almost not happening and the system isn't changing!).