Experimental data accumulated over more than 120 years show not only that diffusion coefficients of impurities ordinarily obey the Arrhenius law in crystalline solids, but also that diffusion pre-exponential factors measured in a same solid increase exponentially with activation energies. This so-called compensation effect has been argued to result from a universal positive linear relationship between entropic contributions and energy barriers to diffusion. However, no physical model of entropy has ever been successfully tested against experimental compensation data. Here, we solve this decades-old problem by demonstrating that atomistically computed harmonic vibrational entropic contributions account for most of compensation effects in silicon and aluminum. We then show that, on average, variations of atomic interactions along diffusion reaction paths simultaneously soften low frequency phonons and stiffen high frequency ones; because relative frequency variations are larger in the lower region of the spectrum, softening generally prevails over stiffening and entropy ubiquitously increases with energy.

One of the leading theories for the origin of life includes the hypothesis according to which life would have evolved as cooperative networks of molecules. Explaining cooperation—and particularly, its emergence in favoring the evolution of life-bearing molecules—is thus a key element in describing the transition from nonlife to life. Using agent-based modeling of the iterated prisoner’s dilemma, we investigate the emergence of cooperative behavior in a stochastic and spatially extended setting and characterize the effects of inheritance and variability. We demonstrate that there is a mutation threshold above which cooperation is—counterintuitively—selected, which drives a dramatic and robust cooperative takeover of the whole system sustained consistently up to the error catastrophe, in a manner reminiscent of typical phase transition phenomena in statistical physics. Moreover, our results also imply that one of the simplest conditional cooperative strategies, “Tit-for-Tat”, plays a key role in the emergence of cooperative behavior required for the origin of life.