Exact nonequilibrium steady state of an open Hubbard chain

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The...

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...