We compute the energetic cost of formation of Janus particle structures. Using an approach that couples particle dynamics to the evolution of fuel concentration in the medium, which we consider to be initially inhomogeneous, we show the different types of emerging structures. The energy dissipated in the formation of such structures is obtained from the entropy production rate, which is a non-monotonic function of the fraction of assembled particles and, thus, different in each self-assembly regime. An analysis of the free energy of these particles allows us to establish a thermodynamic criterion of structure formation based on the behavior of chemical potential as a function of the fraction of assembled particles.

It is shown that the action of an oscillating force on particles moving through a deformable-walled channel causes them to travel greater distances than in the case of a rigid channel. This increase in the transport efficiency is due to an intensification of the stochastic resonance effect observed in corrugated rigid channels, for which the response to the force is maximal for an optimal value of the thermal noise. The distances traveled by the particles are even larger when the oscillation of the micro-channel is synchronized with that of an applied transverse force and also when a constant external force is considered. The phenomenon found could be observed in the transport of particles through elastic porous media, in drug delivery to cancerous tissues, and in the passage of substrates through transporters in biological membranes.Our results indicate that an appropriate channel design and a suitable choice of applied forces lead to optimal scenarios for particle transport.

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