A recently developed framework of information dynamics systematically studies the phenomenon of computation and information processing in complex systems, relating it to critical phenomena, e.g., phase transitions and the edge of chaos. It has been conjectured that at the edge of chaos the distributed computation exhibits a high level of complexity. However, it remains unclear how such complexity is related to physical fluxes which are observed and studied during phase transitions. We consider several examples of near-equilibrium computation (e.g., random Boolean networks and collective motion) as thermodynamic phenomena.  Specifically, we consider the dynamical model of collective motion which undergoes a kinetic phase transition over parameters that control the particles’ alignment: from a “disordered motion” phase, in which particles keep changing direction but occupy a fairly stable collective space, to a “coherent motion” phase, in which particles cohesively move towards a common direction. The control parameters that we consider are the alignment strength among particles and the number of nearest neighbours affecting a particle’s alignment.  This analysis allows us to contrast Fisher information with the curvature of the system's entropy. During the phase transition, where the configuration entropy of the system decreases, the sensitivity of the distributed computation diverges. Overall, the comparison highlights the balancing role of the sensitivity and the uncertainty of computation when the system fluctuates near equilibrium, quantifying the thermodynamic cost of this computation.