Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems

Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate Γ=dLdt and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, L is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.

Phenomenological Models and Peculiarities of Evaluating Fatigue Life of Aluminum Alloys Subjected to Dynamic Non-Equilibrium Processes

Physical-mechanical models for predicting the fatigue life of aluminum alloys D16ChATW and 2024-T351 are proposed and tested. Damage accumulation patterns are established for these alloys in the initial state and after dynamic non-equilibrium processes (DNP) of different intensity that occur at maximum cycle stresses σmax from 340 to 440 MPa, cycle asymmetry coefficients R = 0.1 and load frequency f = 110 Hz. The main model parameters are the initial alloy hardness HV and the limiting parameters of scatter of hardness values m. These parameters are evaluated in the process of cyclic loading with fixed maximum stresses of the cycles. Relative values me are also considered. For the alloys in the initial state, the proposed models are shown to be in good agreement with the experimental results. Conversely, structural changes taking place in alloys after DNP complicate the prediction of their fatigue life.

Out-of-equilibrium processes in crystallization of organic-inorganic perovskites during spin coating

Complex phenomena are prevalent during the formation of materials, which affect their processing-structure-function relationships. Thin films of methylammonium lead iodide (CH3NH3PbI3, MAPI) are processed by spin coating, antisolvent drop, and annealing of colloidal precursors. The structure and properties of transient and stable phases formed during the process are reported, and the mechanistic insights of the underlying transitions are revealed by combining in situ data from grazing-incidence wide-angle X-ray scattering and photoluminescence spectroscopy. Here, we report the detailed insights on the embryonic stages of organic-inorganic perovskite formation. The physicochemical evolution during the conversion proceeds in four steps: i) An instant nucleation of polydisperse MAPI nanocrystals on antisolvent drop, ii) the instantaneous partial conversion of metastable nanocrystals into orthorhombic solvent-complex by cluster coalescence, iii) the thermal decomposition (dissolution) of the stable solvent-complex into plumboiodide fragments upon evaporation of solvent from the complex and iv) the formation (recrystallization) of cubic MAPI crystals in thin film.

Thermodynamics of solid and liquid aluminium

Based on thermodynamic calculations, it is shown that in the temperature range of 298–1273 K, heating and cooling of aluminum are thermodynamically equilibrium processes. When aluminum is heated, the molar volume energy of Gibbs decreases and the molar boundary energy of nanocrystals increases. When aluminum is cooled, the molar volume energy of Gibbs increases and the molar boundary energy of nanocrystals decreases. Liquid aluminum is a nanostructured system. Dendritic microcrystals are formed from nanocrystals. They play a large role in the processes of changing the structure of aluminum during its heating and cooling.

Radioactive decay of $$\mathrm {{}^{90}Sr}$$ in cement: a non-equilibrium first-principles investigation

Cement is an inexpensive and relatively easily manageable material that is used as a last barrier for nuclear waste disposal. Under these conditions, the cement is in contact with low radiation doses, but there is a distinct possibility of being contaminated with radioactive products. Of particular concern is the medium lived half-life product $$\mathrm {{}^{90}Sr}$$ 90 Sr (28.8 years) due to its ability to replace Ca. $$\mathrm {{}^{90}Sr}$$ 90 Sr undergoes $$\beta $$ β -decay to $$\mathrm {{}^{90}Y}$$ 90 Y which, in turn, $$\beta $$ β -decays to stable $$\mathrm {{}^{90}Zr}$$ 90 Zr . In this work, we discuss systematically the chain of non-equilibrium processes that result as a consequence of $$\beta $$ β -decay events in cement. We first use density functional-based methods to study the consequences of the sudden increase of the nuclear charge from $$Z$$ Z to $$Z+1$$ Z + 1 , a possible induced ionization and the perturbation of the surrounding electronic charge. Secondly, we use molecular dynamics simulations to study the recoil of the daughter nucleus. Finally, we discuss the damage caused by the ionization cascade produced during the propagation of the $$\beta $$ β -electron and the resulting chemical and structural perturbation. Graphic Abstract

Causal Information Rate

Information processing is common in complex systems, and information geometric theory provides a useful tool to elucidate the characteristics of non-equilibrium processes, such as rare, extreme events, from the perspective of geometry. In particular, their time-evolutions can be viewed by the rate (information rate) at which new information is revealed (a new statistical state is accessed). In this paper, we extend this concept and develop a new information-geometric measure of causality by calculating the effect of one variable on the information rate of the other variable. We apply the proposed causal information rate to the Kramers equation and compare it with the entropy-based causality measure (information flow). Overall, the causal information rate is a sensitive method for identifying causal relations.

Discrete systems in thermal physics and engineering: a glance from non-equilibrium thermodynamics

Non-equilibrium processes in Schottky systems generate by projection onto the equilibrium subspace reversible accompanying processes for which the non-equilibrium variables are functions of the equilibrium ones. The embedding theorem which guarantees the compatibility of the accompanying processes with the non-equilibrium entropy is proved. The non-equilibrium entropy is defined as a state function on the non-equilibrium state space containing the contact temperature as a non-equilibrium variable. If the entropy production does not depend on the internal energy, the contact temperature changes into the thermostatic temperature also in non-equilibrium, a fact which allows to use temperature as a primitive concept in non-equilibrium. The dissipation inequality is revisited, and an efficiency of generalized cyclic processes beyond the Carnot process is achieved.