A major limitations for many heat engines is that their functioning demands on-line control, and/or an external fitting between environmental parameters (e.g. temperatures of thermal baths) and internal parameters of the engine. We study a model for an adaptive heat engine, where-due to feedback from the functional part-the engine's structure adapts to given thermal baths. Hence no on-line control and no external fitting are needed. The engine can employ unknown resources; it can also adapt to results of its own functioning that makes the bath temperatures closer. We determine thermodynamic costs of adaptation and relate them to the prior information available about the environment. We also discuss informational constraints on the structure-function interaction that are necessary for adaptation.

In this paper, we discuss three different response strategies to a disease outbreak and their economic implications in an age-structured population. We have utilized the classical age structured SIR-model, thus assuming that recovered people will not be infected again. Available resource dynamics is governed by the well-known logistic growth model, in which the reproduction coefficient depends on the disease outbreak spreading dynamics. We further investigate the feedback interaction of the disease spread dynamics and resource growth dynamics with the premise that the quality of treatment depends on the current economic situation. The very inclusion of mortality rates and economic considerations in the same model may be incongruous under certain positions, but in this model, we take a “realpolitik” approach by exploring all of these factors together as it is done in reality.

Statistical mechanics is based on the interplay between energy and entropy. Here we formalize this interplay via axiomatic bargaining theory (a branch of cooperative game theory), where entropy and negative energy are represented by utilities of two different players. Game-theoretic axioms provide a solution to the thermalization problem, which is complementary to existing physical approaches. We predict thermalization of a nonequilibrium statistical system employing the axiom of affine covariance, related to the freedom of changing initial points and dimensions for entropy and energy, together with the contraction invariance of the entropy-energy diagram. Thermalization to negative temperatures is allowed for active initial states. Demanding a symmetry between players determines the final state to be the Nash solution (well known in game theory), whose derivation is improved as a by-product of our analysis. The approach helps to retrodict nonequilibrium predecessors of a given equilibrium state.