Recent studies of active matter have stimulated interest in the driven self-assembly of complex structures. Phenomenological modeling of particular examples has yielded insight, but general thermodynamic principles unifying the rich diversity of behaviors observed have been elusive. Here, we study the stochastic search of a toy chemical space by a collection of reacting Brownian particles subject to periodic forcing. We observe the emergence of an adaptive resonance in the system matched to the drive frequency, and show that the increased work absorption by these resonant structures is key to their stabilization. Our findings are consistent with a recently proposed thermodynamic mechanism for far-from-equilibrium self-organization.
Whether by virtue of being prepared in a slowly relaxing, high-free energy initial condition, or because they are constantly dissipating energy absorbed from a strong external drive, many systems subject to thermal fluctuations are not expected to behave in the way they would at thermal equilibrium. Rather, the probability of finding such a system in a given microscopic arrangement may deviate strongly from the Boltzmann distribution, raising the question of whether thermodynamics still has anything to tell us about which arrangements are the most likely to be observed. In this work, we build on past results governing nonequilibrium thermodynamics and define a generalized Helmholtz free energy that exactly delineates the various factors that quantitatively contribute to the relative probabilities of different outcomes in far-from-equilibrium stochastic dynamics. By applying this expression to the analysis of two examples—namely, a particle hopping in an oscillating energy landscape and a population composed of two types of exponentially growing self-replicators—we illustrate a simple relationship between outcome-likelihood and dissipative history. In closing, we discuss the possible relevance of such a thermodynamic principle for our understanding of self-organization in complex systems, paying particular attention to a possible analogy to the way evolutionary adaptations emerge in living things.