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In this work we investigate greedy energy sequences on the unit circle forthe logarithmic and Riesz potentials. By definition, if $(a_n)_{n=0}^{\infty}$is a greedy $s$-energy sequence on the unit circle, the Riesz potential$U_{N,s}(x):=\sum_{k=0}^{N-1}|a_k-x|^{-s}$, $s>0$, generated by the first $N$points of the sequence attains its minimum value at the point $a_{N}$, forevery $N\geq 1$. In the case $s=0$ we minimize instead the logarithmicpotential $U_{N,0}(x):=-\sum_{k=0}^{N-1}\log |a_{k}-x|$. We analyze theasymptotic properties of these extremal values $U_{N,s}(a_N)$, studyingseparately the cases $s=0$, $0<s<1$, $s=1$, and $s>1$. We obtain second-orderasymptotic formulas for $U_{N,s}(a_N)$ in the cases $s=0$, $0<s<1$, and $s=1$(the corresponding first-order formulas are well known). A first-order resultfor $s>1$ is proved, and it is shown that the normalized sequence$U_{N,s}(a_N)/N^s$ is bounded and divergent in this case. We also consider,briefly, greedy energy sequences in which the minimization condition isrequired starting from the point $a_{p+1}$ (instead of the point $a_{1}$ aspreviously stated), for some $p\geq 1$. For this more general class of greedysequences, we prove a first-order asymptotic result for $0\leq s<1$.

Asymptotics of the minimum values of Riesz and logarithmic potentials generated by greedy energy sequences on the unit circle