Stochastic and information-thermodynamic structures of population dynamics in a fluctuating environment

Thermodynamic optimization subsumed in stability phenomena

In the present paper the possibility of an energetic self-optimization as a consequence of thermodynamic stability is addressed. This feature is analyzed in a low dissipation refrigerator working in an optimized trade-off regime (the so-called Omega function). The relaxation after a perturbation around the stable point indicates that stability is linked to trajectories in which the thermodynamic performance is improved. Furthermore, a limited control over the system is analyzed through consecutive external random perturbations. The statistics over many cycles corroborates the preference for a better thermodynamic performance. Endoreversible and irreversible behaviors play a relevant role in the relaxation trajectories (as well as in the statistical performance of many cycles experiencing random perturbations). A multi-objective optimization reveals that the well-known endoreversible limit works as an attractor of the system evolution coinciding with the Pareto front, which represents the best energetic compromise among efficiency, entropy generation, cooling power, input power and the Omega function. Meanwhile, near the stable state, performance and stability are dominated by an irreversible behavior.

Tuning environmental timescales to evolve and maintain generalists

Natural environments can present diverse challenges, but some genotypes remain fit across many environments. Such "generalists" can be hard to evolve, outcompeted by specialists fitter in any particular environment. Here, inspired by the search for broadly neutralizing antibodies during B cell affinity maturation, we demonstrate that environmental changes on an intermediate timescale can reliably evolve generalists, even when faster or slower environmental changes are unable to do so. We find that changing environments on timescales comparable with evolutionary transients in a population enhance the rate of evolving generalists from specialists, without enhancing the reverse process. The yield of generalists is further increased in more complex dynamic environments, such as a "chirp" of increasing frequency. Our work offers design principles for how nonequilibrium fitness "seascapes" can dynamically funnel populations to genotypes unobtainable in static environments.

Energetic Self-Optimization Induced by Stability in Low-Dissipation Heat Engines

The local stability of a weakly dissipative heat engine is analyzed and linked to an energetic multi-objective optimization perspective. This constitutes a novel issue in the unified study of cyclic energy converters, opening the perspective to the possibility that stability favors self-optimization of thermodynamic quantities including efficiency, power and entropy generation. To this end, a dynamics simulating the restitution forces, which mimics a harmonic potential, bringing the system back to the steady state is analyzed. It is shown that relaxation trajectories are not arbitrary but driven by the improvement of several energetic functions. Insights provided by the statistical behavior of consecutive random perturbations show that the irreversible behavior works as an attractor for the energetics of the system, while the endoreversible limit acts as an upper bound and the Pareto front as a global attractor. Fluctuations around the operation regime reveal a difference between the behavior coming from fast and slow relaxation trajectories: while the former are associated to an energetic self-optimization evolution, the latter are ascribed to better performances. The self-optimization induced by stability and the possible use of instabilities in the operation regime to improve the energetic performance might usher into new useful perspectives in the control of variables for real engines.

Optimization induced by stability and the role of limited control near a steady state

A relationship between stability and self-optimization is found for weakly dissipative heat devices. The effect of limited control on operation variables around an steady state is such that, after instabilities, the paths toward relaxation are given by trajectories stemming from restitution forces which improve the system thermodynamic performance (power output, efficiency, and entropy generation). Statistics over random trajectories for many cycles shows this behavior as well. Two types of dynamics are analyzed, one where an stability basin appears and another one where the system is globally stable. Under both dynamics there is an induced trend in the control variables space due to stability. In the energetic space this behavior translates into a preference for better thermodynamic states, and thus stability could favor self-optimization under limited control. This is analyzed from the multiobjective optimization perspective. As a result, the statistical behavior of the system is strongly influenced by the Pareto front (the set of points with the best compromise between several objective functions) and the stability basin. Additionally, endoreversible and irreversible behaviors appear as very relevant limits: The first one is an upper bound in energetic performance, connected with the Pareto front, and the second one represents an attractor for the stochastic trajectories.

Many-body perturbation theory and fluctuation relations for interacting population dynamics

Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments. However, it is quite difficult to insist on a general statement on living organisms since mathematical models heavily depend on phenomena that we focus on. Recently, it was reported that the fluctuation relations on the fitness of living organisms held for a quite general problem setting. But, interactions between organisms were not incorporated in the problem setting, though interaction plays critical roles in collective phenomena in physics and population dynamics. In this paper, we propose interacting models for population dynamics and provide the perturbative theory of population dynamics. Then, we derive the variational principle and fluctuation relations for interacting population dynamics.

Fitness response relation of a multitype age-structured population dynamics

We construct a pathwise formulation for a multitype age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a tradeoff relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.