scholarly journals Life as we know it

2013 ◽  
Vol 10 (86) ◽  
pp. 20130475 ◽  
Author(s):  
Karl Friston
Keyword(s):  
Bayesian Inference ◽  
Structural Integrity ◽  
Energy Functional ◽  
Self Organization ◽  
Random Dynamical System ◽  
Markov Blanket ◽  
Free Energy Functional ◽  
Internal States ◽  
Statistical Sense ◽  
Primordial Soup

This paper presents a heuristic proof (and simulations of a primordial soup) suggesting that life—or biological self-organization—is an inevitable and emergent property of any (ergodic) random dynamical system that possesses a Markov blanket. This conclusion is based on the following arguments: if the coupling among an ensemble of dynamical systems is mediated by short-range forces, then the states of remote systems must be conditionally independent. These independencies induce a Markov blanket that separates internal and external states in a statistical sense. The existence of a Markov blanket means that internal states will appear to minimize a free energy functional of the states of their Markov blanket. Crucially, this is the same quantity that is optimized in Bayesian inference. Therefore, the internal states (and their blanket) will appear to engage in active Bayesian inference. In other words, they will appear to model—and act on—their world to preserve their functional and structural integrity, leading to homoeostasis and a simple form of autopoiesis.

scholarly journals Markov blankets, information geometry and stochastic thermodynamics

2019 ◽  
Vol 378 (2164) ◽  
pp. 20190159 ◽  
Author(s):  
Thomas Parr ◽  
Lancelot Da Costa ◽  
Karl Friston
Keyword(s):  
Gradient Flow ◽  
Information Geometry ◽  
Random Dynamical System ◽  
Stochastic Thermodynamics ◽  
Energy Principle ◽  
Markov Blanket ◽  
Autonomous Computing ◽  
Internal States ◽  
Weakly Mixing ◽  
The Relationship

This paper considers the relationship between thermodynamics, information and inference. In particular, it explores the thermodynamic concomitants of belief updating, under a variational (free energy) principle for self-organization. In brief, any (weakly mixing) random dynamical system that possesses a Markov blanket—i.e. a separation of internal and external states—is equipped with an information geometry. This means that internal states parametrize a probability density over external states. Furthermore, at non-equilibrium steady-state, the flow of internal states can be construed as a gradient flow on a quantity known in statistics as Bayesian model evidence. In short, there is a natural Bayesian mechanics for any system that possesses a Markov blanket. Crucially, this means that there is an explicit link between the inference performed by internal states and their energetics—as characterized by their stochastic thermodynamics. This article is part of the theme issue ‘Harmonizing energy-autonomous computing and intelligence’.

scholarly journals DNA self-organization controls valence in programmable colloid design

2021 ◽  
Vol 118 (46) ◽  
pp. e2112604118
Author(s):  
Angus McMullen ◽  
Sascha Hilgenfeldt ◽  
Jasna Brujic
Keyword(s):  
Free Energy ◽  
Protein Interactions ◽  
Energy Functional ◽  
Molecular Organization ◽  
Self Organization ◽  
Mobile Dna ◽  
Free Energy Functional ◽  
Patchy Particles ◽  
Equilibrium Size ◽  
Complex Architectures

Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence—the number of interparticle bonds—is a prerequisite for the assembly of complex architectures. The assembly can be directed via solid “patchy” particles with prescribed geometries to make, for example, a colloidal diamond. We demonstrate here that the nanoscale ordering of individual molecular linkers can combine to program the structure of microscale assemblies. Specifically, we experimentally show that covering initially isotropic microdroplets with N mobile DNA linkers results in spontaneous and reversible self-organization of the DNA into Z(N) binding patches, selecting a predictable valence. We understand this valence thermodynamically, deriving a free energy functional for droplet–droplet adhesion that accurately predicts the equilibrium size of and molecular organization within patches, as well as the observed valence transitions with N. Thus, microscopic self-organization can be programmed by choosing the molecular properties and concentration of binders. These results are widely applicable to the assembly of any particle with mobile linkers, such as functionalized liposomes or protein interactions in cell–cell adhesion.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Droplet minimizers for the Gates–Lebowitz–Penrose free energy functional

Nonlinearity ◽  
2009 ◽  
Vol 22 (12) ◽  
pp. 2919-2952 ◽  
Author(s):  
E A Carlen ◽  
M C Carvalho ◽  
R Esposito ◽  
J L Lebowitz ◽  
R Marra
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Free Energy Functional

scholarly journals Droplet minimizers for the Cahn-Hilliard free energy functional

2006 ◽  
Vol 16 (2) ◽  
pp. 233-264 ◽  
Author(s):  
E. A. Carlen ◽  
M. C. Carvalho ◽  
R. Esposito ◽  
J. L. Lebowitz ◽  
R. Marra
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Free Energy Functional

scholarly journals Homogenization of composite ferromagnetic materials

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150365 ◽  
Author(s):  
François Alouges ◽  
Giovanni Di Fratta
Keyword(s):  
Free Energy ◽  
Ferromagnetic Material ◽  
Energy Functional ◽  
Ferromagnetic Materials ◽  
Rigorous Derivation ◽  
Free Energy Functional ◽  
Landau Free Energy ◽  
Ferromagnetic Body ◽  
The Media

The objective of this paper is to perform, by means of Γ - convergence and two-scale convergence , a rigorous derivation of the homogenized Gibbs–Landau free energy functional associated with a composite periodic ferromagnetic material, i.e. a ferromagnetic material in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the Gibbs–Landau free energy functional, as the period over which the heterogeneities are distributed inside the ferromagnetic body shrinks to zero.

MODIFIED VAN DER WAALS MODEL FOR SURFACE-MELTING DISCUSSION

1995 ◽  
Vol 02 (06) ◽  
pp. 773-785 ◽  
Author(s):  
L. WOJTCZAK ◽  
J.H. RUTKOWSKI
Keyword(s):  
Thermodynamic Potential ◽  
Van Der Waals ◽  
Mean Field Theory ◽  
Mean Field ◽  
Energy Functional ◽  
Surface Melting ◽  
Free Energy Functional ◽  
Thickness Profile ◽  
The Mean ◽  
Surface Liquid

The thermodynamic potential governing the surface-melting, considered in terms of the crystallinity and its profile is related to the Gibbs free-energy functional, leads to van der Waals equation of state. The presented construction allows us to determine the mean-field coefficients by their reference to material constants. The model is applied to the surface-melting discussion within the Landau-type mean-field theory of phase-transitions. In particular, the surface-melting temperature is estimated and temperature dependence of the surface liquid-like layer thickness profile is obtained.

Classical and semiclassical dynamics in statistical environments with a mixed dynamical and statistical representation

2016 ◽  
Vol 18 (3) ◽  
pp. 1771-1785 ◽  
Author(s):  
Kazuo Takatsuka ◽  
Kentaro Matsumoto
Keyword(s):  
Free Energy ◽  
Real Time ◽  
Energy Functional ◽  
Basic Theory ◽  
Chemical Dynamics ◽  
Functional Surface ◽  
Spatial Gradients ◽  
Free Energy Functional ◽  
Statistical Representation ◽  
Semiclassical Dynamics

We present a basic theory to study real-time chemical dynamics embedded in a statistically treated large environment. It is shown that dynamically treated molecules should run on the free-energy functional surface, if and only if the spatial gradients of temperature functional are all zero.

scholarly journals Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study

2021 ◽  
Author(s):  
Razvan-Dumitru Ceuca
Keyword(s):  
Free Energy ◽  
Additional Term ◽  
Energy Functional ◽  
Free Energies ◽  
Cubic Symmetry ◽  
Surface Anchoring ◽  
Free Energy Functional ◽  
Different Types ◽  
Embedded Particles ◽  
Anchoring Energy

We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and then we compute the free effective energy of the composite material. In the cubic symmetry case, we impose different types of surface anchoring energy densities, such as quartic, Rapini-Papoular or more general versions, and, in this case, we show that we can tune any coefficient from the corresponding bulk potential, especially the phase transition temperature. In the case with loss of cubic symmetry, we prove similar results in which the effective free energy functional has now an additional term, which describes a change in the preferred alignment of the liquid crystal particles inside the domain. Moreover, we compute the rate of convergence for how fast the surface energies converge to the homogenised one and also for how fast the minimisers of the free energies tend to the minimiser of the homogenised free energy.

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