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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]
Equilibrant force. In mechanics, an equilibrant force is a force which brings a body into mechanical equilibrium. [1] According to Newton's second law, a body has zero acceleration when the vector sum of all the forces acting upon it is zero:
Unit cell definition using parallelepiped with lengths a, b, c and angles between the sides given by α, β, γ [1]. A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.
In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. [ citation needed ] Partition functions are functions of the thermodynamic state variables , such as the temperature and volume .
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 ...
In condensed matter physics, relaxation is usually studied as a linear response to a small external perturbation. Since the underlying microscopic processes are active even in the absence of external perturbations, one can also study "relaxation in equilibrium" instead of the usual "relaxation into equilibrium" (see fluctuation-dissipation theorem).
The equilibrium state of a thermodynamic system is described by specifying its "state". The state of a thermodynamic system is specified by a number of extensive quantities , the most familiar of which are volume , internal energy , and the amount of each constituent particle ( particle numbers ).
In the case of chemical reactions this is usually the number of particles or mole fractions, subject to the conservation of elements. At equilibrium, these will take on their equilibrium values, and the internal energy will be a function only of the chosen value of entropy . By the definition of the Legendre transform, the Helmholtz free energy ...