  Entropy production characterizes the thermodynamic irreversibility and
reflects the amount of heat dissipated into the environment and free energy
lost in nonequilibrium systems. According to the thermodynamic uncertainty
relation, we propose a deterministic method to estimate the entropy production
from a single trajectory of system states. We explicitly and approximately
compute an optimal current that yields the tightest lower bound using
predetermined basis currents. Notably, the obtained tightest lower bound is
intimately related to the multidimensional thermodynamic uncertainty relation.
By proving the saturation of the thermodynamic uncertainty relation in the
short-time limit, the exact estimate of the entropy production can be obtained
for overdamped Langevin systems, irrespective of the underlying dynamics. For
Markov jump processes, because the attainability of the thermodynamic
uncertainty relation is not theoretically ensured, the proposed method provides
the tightest lower bound for the entropy production. When entropy production is
the optimal current, a more accurate estimate can be further obtained using the
integral fluctuation theorem. We illustrate the proposed method using three
systems: a four-state Markov chain, a periodically driven particle, and a
multiple bead-spring model. The estimated results in all examples empirically
verify the effectiveness and efficiency of the proposed method.
