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Consequently, the object is in a state of static mechanical equilibrium. In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. [1]: 39 By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. [1]: 45–46 [2]
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
An example of this is quasi-static expansion of a mixture of hydrogen and oxygen gas, where the volume of the system changes so slowly that the pressure remains uniform throughout the system at each instant of time during the process. [2] Such an idealized process is a succession of physical equilibrium states, characterized by infinite ...
The static equilibrium of a particle is an important concept in statics. A particle is in equilibrium only if the resultant of all forces acting on the particle is equal to zero. In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations, where the sums of forces in all three directions are equal ...
A quasi-static thermodynamic process can be visualized by graphically plotting the path of idealized changes to the system's state variables. In the example, a cycle consisting of four quasi-static processes is shown. Each process has a well-defined start and end point in the pressure-volume state space.
where T is temperature, S is entropy, P is pressure, μ is the chemical potential, N is the number of particles in the gas, and the volume has been written as V=Ax. Since the system is closed, the particle number N is constant and a small change in the energy of the system would be given by: = +
D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing forces of inertia which, when added to the applied forces in a system, result in dynamic equilibrium. [1] [2] D'Alembert's principle can be applied in cases of kinematic constraints that depend on velocities.
The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as ...