Søren Nors Nielsen, Felix Müller

Entropy 2023, 25(9), 1288

In the last few decades, the number of published papers that include search terms such as thermodynamics, entropy, ecology, and ecosystems has grown rapidly. Recently, background research carried out during the development of a paper on “thermodynamics in ecology” revealed huge variation in the understanding of the meaning and the use of some of the central terms in this field—in particular, entropy. This variation seems to be based primarily on the differing educational and scientific backgrounds of the researchers responsible for contributions to this field. Secondly, some ecological subdisciplines also seem to be better suited and applicable to certain interpretations of the concept than others. The most well-known seems to be the use of the Boltzmann–Gibbs equation in the guise of the Shannon–Weaver/Wiener index when applied to the estimation of biodiversity in ecology. Thirdly, this tendency also revealed that the use of entropy-like functions could be diverted into an area of statistical and distributional analyses as opposed to real thermodynamic approaches, which explicitly aim to describe and account for the energy fluxes and dissipations in the systems. Fourthly, these different ways of usage contribute to an increased confusion in discussions about efficiency and possible telos in nature, whether at the developmental level of the organism, a population, or an entire ecosystem. All the papers, in general, suffer from a lack of clear definitions of the thermodynamic functions used, and we, therefore, recommend that future publications in this area endeavor to achieve a more precise use of language. Only by increasing such efforts it is possible to understand and resolve some of the significant and possibly misleading discussions in this area.

Read the full article at: www.mdpi.com

Guim Aguadé-Gorgorió, Jean-François Arnoldi, Matthieu Barbier, Sonia Kéfi

Many natural and man-made systems, from financial markets to ecosystems or the human brain, are built from multiple interconnected units. This complex high-dimensionality hinders our capacity to understand and predict the dynamics, functioning and fragility of these systems. One fragility scenario, particularly relevant to ecological communities of interacting species, concerns so-called regime shifts: abrupt and unexpected transitions from healthy, species-rich communities towards states of degraded ecosystem function and services. The accepted explanation for these shifts is that they arise as abrupt transitions between alternative stable states: multiple stable configurations of a system under the same internal and external conditions. These alternative states are well-understood in low-dimensional systems, but how they upscale with system complexity remains a debated question. In the present work we investigate the emergence of multiple stable states in a number of complex system models. We find that high-dimensional models with random interactions can unfold at least four different regimes of multistability, each emerging under a specific interaction scheme. More importantly, each multistability regime leaves a distinct and quantifiable fingerprint, providing a framework to analyze experimental evidence of abrupt shifts. By bridging previous results and studying multistability regimes, their fingerprints and their correlation with empirical evidence in ecology, our study helps define a common ground to understand and classify multiple stable states in complex systems.

Read the full article at: www.biorxiv.org

J. G. Oliveira, S. N. Dorogovtsev, J. F. F. Mendes

We delve into the statistical properties of regions within complex networks that are distant from vertices with high centralities, such as hubs or highly connected clusters. These remote regions play a pivotal role in shaping the asymptotic behaviours of various spreading processes and the features of associated spectra. We investigate the probability distribution P≥m(s) of the number s of vertices located at distance m or beyond from a randomly chosen vertex in an undirected network. Earlier, this distribution and its large m asymptotics 1/s2 were obtained theoretically for undirected uncorrelated networks [S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin, Nucl. Phys. B 653 (2003) 307]. Employing numerical simulations and analysing empirical data, we explore a wide range of real undirected networks and their models, including trees and loopy networks, and reveal that the inverse square law is valid even for networks with strong correlations. We observe this law in the networks demonstrating the small-world effect and containing vertices with degree 1 (so-called leaves or dead ends). We find the specific classes of networks for which this law is not valid. Such networks include the finite-dimensional networks and the networks embedded in finite-dimensional spaces. We notice that long chains of nodes in networks reduce the range of m for which the inverse square law can be spotted. Interestingly, we detect such long chains in the remote regions of the undirected projection of a large Web domain.

Read the full article at: arxiv.org

Artemy Kolchinsky

Phys. Rev. E 108, 034101

We consider the minimal thermodynamic cost of an individual computation, where a single input $x$is mapped to a single output $y$. In prior work, Zurek proposed that this cost was given by $K\left(x\right|y)$, the conditional Kolmogorov complexity of $x$ given $y$ (up to an additive constant that does not depend on $x$ or $y$). However, this result was derived from an informal argument, applied only to deterministic computations, and had an arbitrary dependence on the choice of protocol (via the additive constant). Here we use stochastic thermodynamics to derive a generalized version of Zurek’s bound from a rigorous Hamiltonian formulation. Our bound applies to all quantum and classical processes, whether noisy or deterministic, and it explicitly captures the dependence on the protocol. We show that $K\left(x\right|y)$ is a minimal cost of mapping $x$ to $y$ that must be paid using some combination of heat, noise, and protocol complexity, implying a trade-off between these three resources. Our result is a kind of “algorithmic fluctuation theorem” with implications for the relationship between the second law and the Physical Church-Turing thesis.

Read the full article at: link.aps.org