Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First it is shown that the probability distribution p Γ of the underlying microscopic phase space trajectories Γ over a time interval of length τ satisfies p Γ ∝ exp(τσ Γ /2k B )where σ Γ is the time-averaged rate of entropy production of Γ. Three consequences of this result are then derived : (1) the Fluctuation Theorem, which describes the exponentially declining probability of deviations from the 2 nd law of thermodynamics as τ→∞ ; (2) the selection principle of maximum entropy production for non-equilibrium stationary states, empirical support for which has been found in studies of phenomena as diverse as the Earth's climate and crystal growth morphology ; and (3) the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The explanation of these results on general information theoretic grounds underlines their relevance to a broad class of stationary, non-equilibrium systems. In turn, the accumulating empirical evidence for these results lends support to Jaynes' formalism as a common predictive framework for equilibrium and non-equilibrium statistical mechanics.

In 1965 Jaynes provided an intuitively simple proof of the 2 nd law of thermodynamics as a general requirement for any macroscopic transition to be experimentally reproducible. His proof was based on Boltzmann's formula S = klnW and the dynamical invariance of the phase volume W for isolated systems (Liouville's theorem). Here Jaynes' proof is extended to show that Liouville's theorem also implies maximum entropy production (MaxEP) for the stationary states of open, non-equilibrium systems. According to this proof, MaxEP stationary states are selected because they can exist within a greater number of environments than any other stationary states. Liouville's theorem applied to isolated systems also gives an intuitive derivation of the fluctuation theorem in a form consistent with an earlier conjecture by Jaynes on the probability of violations of the 2 nd law. The present proof of MaxEP, while largely heuristic, suggests an approach to establishing a more fundamental basis for MaxEP using Jaynes' maximum entropy formulation of statistical mechanics.

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Summary Based on short‐term experiments, many plant growth models – including those used in global change research – assume that an increase in temperature stimulates plant respiration (R) more than photosynthesis (P), leading to an increase in the R/P ratio. Longer‐term experiments, however, have demonstrated that R/P is relatively insensitive to growth temperature. We show that both types of temperature response may be reconciled within a simple substrate‐based model of plant acclimation to temperature, in which respiration is effectively limited by the supply of carbohydrates fixed through photosynthesis. The short‐term, positive temperature response of R/P reflects the transient dynamics of the nonstructural carbohydrate and protein pools; the insensitivity of R/P to temperature on longer time‐scales reflects the steady‐state behaviour of these pools. Thus the substrate approach may provide a basis for predicting plant respiration responses to temperature that is more robust than the current modelling paradigm based on the extrapolation of results from short‐term experiments. The present model predicts that the acclimated R/P depends mainly on the internal allocation of carbohydrates to protein synthesis, a better understanding of which is therefore required to underpin the wider use of a constant R/P as an alternative modelling paradigm in global change research.

We review approaches to predicting carbon and nitrogen allocation in forest models in terms of their underlying assumptions and their resulting strengths and limitations. Empirical and allometric methods are easily developed and computationally efficient, but lack the power of evolution-based approaches to explain and predict multifaceted effects of environmental variability and climate change. In evolution-based methods, allocation is usually determined by maximization of a fitness proxy, either in a fixed environment, which we call optimal response (OR) models, or including the feedback of an individual's strategy on its environment (game-theoretical optimization, GTO). Optimal response models can predict allocation in single trees and stands when there is significant competition only for one resource. Game-theoretical optimization can be used to account for additional dimensions of competition, e.g., when strong root competition boosts root allocation at the expense of wood production. However, we demonstrate that an OR model predicts similar allocation to a GTO model under the root-competitive conditions reported in free-air carbon dioxide enrichment (FACE) experiments. The most evolutionarily realistic approach is adaptive dynamics (AD) where the allocation strategy arises from eco-evolutionary dynamics of populations instead of a fitness proxy. We also discuss emerging entropy-based approaches that offer an alternative thermodynamic perspective on allocation, in which fitness proxies are replaced by entropy or entropy production. To help develop allocation models further, the value of wide-ranging datasets, such as FLUXNET, could be greatly enhanced by ancillary measurements of driving variables, such as water and soil nitrogen availability.