Fig. 3
Extracting current fluctuations from trajectories. a A realization of a long trajectory diffusing through configuration space. The macroscopic current is computing by choosing a vector field d(x), here chosen as the thermodynamic force field F(x). b On the microscopic scale, the trajectory may be modeled as discrete jumps between neighboring lattice sites (here labeled with symbols: lozenge, star, square, …). The continuous-space vector field is decomposed into components along the direction of possible jumps, i.e., d evaluated at the black triangle site can be expressed in terms of the weight d◊,▲ associated with a jump from the black triangle to the white diamond. c A realization of the trajectory gives a single value of the empirical current jd. By recording many realizations, the empirical current distribution P(jd) is sampled to give 〈jd〉 and Var(jd) (inset). In the case that d = F, the mean slope of this accumulated current is the average entropy production rate. d The empirical current for a single realization is constructed as the sum of the d weights for each microscopic transition of the jump process
