  The energy change dE_k for the kth microstate is erroneously equated with the
external work done on the microstate. It ignores the ubiquitous internal energy
change d_iW_k due to force imbalance between the internal and external forces.
We show that this contribution is present even in a reversible process, which
is a surprise. We show that the correct identification is dE_k=-dW_k, where
dW_k is the generalized work done by the microstate. We prove that the
thermodynamic average of the internal work gives dissipation and is not
captured by the external work. The latter effectively sets d_iW_k =0 and
results in no dissipation. Using dW_k to account for irreversibility, we obtain
a new work relation that works even for free expansion, where the Jarzynski
equality fails. In the new work relation, dW_k depends only on the energies of
the initial and final states and not on the actual process. This makes the new
relation very different from the Jarzynski equality. The correction has
far-reaching consequences and requires reassessment of current applications of
external work in theoretical physics.
