Entropy of deterministic trajectory via trajectories ensemble

We present a formulation of the single-trajectory entropy using the trajectories ensemble. The single-trajectory entropy is affected by its surrounding trajectories via the distribution function. The single-trajectory entropies are studied in two typical potentials, i.e., harmonic potential and double-well potential, and in viscous environment by interacting trajectory method. The results of the trajectory methods are in agreement well with the numerical methods (Monte Carlo simulation and difference equation). The single-trajectory entropies increasing (decreasing) could be caused by absorption (emission) heat from (to) the thermal environment. Also, some interesting trajectories, which correspond to the rare evens in the processes, are demonstrated.