Arrhenius plots, which are used to represent the effects of temperature on the rates of chemical and biophysical processes and on various transport phenomena in materials science, may exhibit deviations from linearity. Account of curvature is provided here by a formula which involves a deformation of the exponential function, of the kind recently encountered in treatments of non-extensivity in statistical mechanics. We present here examples on diverse topics - respiration rates of plants, speed of gliding of bacteria, quantum mechanical tunneling in a chemical reaction - illustrating the variety of possible applications and the additional insight that can be gained. (C) 2010 Elsevier B. V. All rights reserved.