Active Matter, Microreversibility, and Thermodynamics
Current densities and corresponding affinities or thermodynamic forces in the active suspension: is the reaction rate density introduced in equation (33) corresponding to the affinity (51), and are the molecular current densities of fuel and product , is the translational current density of colloids given by equation (45), is the rotational current density of colloids given by equation (46). The translational and rotational current densities of colloids form the five-dimensional current density (55) according to . Similarly, the translational and rotational affinities of colloids form the five-dimensional affinity (54). denotes the inverse temperature, the chemical potentials, the gradient in Euclidean space, and the rotational gradient (40). We note that colloidal motors with the given orientation are considered as so many independent species in the free energy (47), which is expressed by equation (56).