  In this paper, we investigate the functional central limit theorem for
stochastic processes associated to partial sums of additive functionals of
reversible Markov chains with general spate space, under the normalization
standard deviation of partial sums. For this case, we show that the functional
central limit theorem is equivalent to the fact that the variance of partial
sums is regularly varying with exponent 1 and the partial sums satisfy the CLT.
It is also equivalent to the conditional CLT.
