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In thermodynamics, equivalent to the growth of entropy in an adiabatic body is the decrease of the available free energy in a body whose boundary is kept as a constant temperature. In this study, we will show that there is also a competition between entropy and energy in the static elastic contact problems, which was found in the procedure of computing contact forces in the finite element model of contact problems. The potential contact nodes that are on the potential contact boundary are considered as a canonical ensemble of statistical physics, the nodal contact forces are normalized with a surrogate model of the primal model of contact problem, and a normalized nodal contact force is treated as the probability of a system occupying a microstate in statistical physics. Then analogous to the probability distribution that is obtained by maximizing the Gibbs entropy subject to the normalization condition of probability and the expectation value of system energy, the explicit formulation of normalized nodal contact forces is obtained by maximizing the entropy under the constraints of expectation of work done by the contact forces and nonpenetration conditions on the potential contact surface. An iterative algorithm for computing contact forces is constructed based on two principles - the principle of minimum potential energy and principle of maximum entropy. They are alternately applied in the iterative procedure, with the initial values of normalized nodal contact forces,  to find displacement with the principle of minimum potential energy, then to find an updated potential nodal contact force with the principle of maximum entropy using the displacement, keep the iteration until the termination condition is met. Examples show that the potential energy is increasing, and the entropy is decreasing throughout the iteration, this is contrary to the general understanding of entropy, that is, the potential energy should be decreased, and the entropy should be increased. This is because the "environment" of each step to calculate potential energy or entropy is different, even in an "environment" determined by nodal contact forces or displacements, the entropy reaches to the maximum or the potential energy reaches to the minimum, but in the whole process, the entropy is decreasing, and the potential energy is increasing, which shows a competitive relationship between the two concepts.