Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems

2014 ◽  
Vol 141 (10) ◽  
pp. 105104 ◽  
Author(s):  
Wei Wu ◽  
Jin Wang
Keyword(s):  
Dynamical Systems ◽  
Equilibrium Thermodynamics ◽  
Stochastic Dynamical Systems ◽  
Spatially Inhomogeneous ◽  
Landscape Theory ◽  
Non Equilibrium

Coherent phenomena in stochastic dynamical systems

1999 ◽  
Vol 169 (2) ◽  
pp. 171 ◽  
Author(s):  
Valerii I. Klyatskin ◽  
D. Gurarie
Keyword(s):  
Dynamical Systems ◽  
Stochastic Dynamical Systems

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

scholarly journals Contraction of polymer gels created by the activity of molecular motors

Soft Matter ◽  
2019 ◽  
Vol 15 (22) ◽  
pp. 4467-4475 ◽  
Author(s):  
Mattia Bacca ◽  
Omar A. Saleh ◽  
Robert M. McMeeking
Keyword(s):  
Mechanical Behavior ◽  
Molecular Motors ◽  
Polymer Gels ◽  
Polymer Gel ◽  
Equilibrium Thermodynamics ◽  
Non Equilibrium

We propose a theory based on non-equilibrium thermodynamics to describe the mechanical behavior of an active polymer gel created by the inclusion of molecular motors in its solvent.

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