This work is based on a weaving together of recent results from three mathematical disciplines: the ergodic theory of dynamical systems, stochastic processes, and the response theory
of nonequilibrium dynamical systems.
Our work compares the predictions of a theory
of nonequilibrium phase transitions with nonstandard statistical signatures of earthquake complex scaling behaviors.
The nature
of these nonequilibrium processes, whatever they are, do not appear in your equation.
Fred, are you distinguishing the stratosphere temperature — during the period
of nonequilibrium from — during the new equilibrium period after CO2 stops increasing and the warming has leveled off at a higher temperature?
In the field
of nonequilibrium dynamics, there are interesting phenomena, such as the Belousov Zhabotinsky systems, which exhibit complex ordered features (going under the general field of self - organising systems).
Do you believe the MEP principle can't be generalized to another, deeper extremum principle which would hold to a class
of nonequilibrium thermodynamic systems terrestrial climate belongs to?
Ab Initio Calculations
of Nonequilibrium Coupled Carrier and Phonon Dynamics.
Not exact matches
As the concentration
of reagent is increased, the system would be taken beyond the chemical instability, and there would be two equally probable
nonequilibrium steady states.
However, if fluctuations (that exceed certain minimum values in magnitude and extent) are included, then the instability
of the initial (Nigerian) steady state is demonstrated, and the system approaches one (Irish) or the other (Ivory Coastian)
of the two stable
nonequilibrium steady states.
An interesting question is: how does the system decide which
of the two possible
nonequilibrium steady states to approach?
11 Richard M. Noyes and Richard J. Field, «Mechanisms
of Chemical Oscillators: Experimental Examples,» Accounts
of Chemical Research 10 (1977), 273 - 80; Joel Keizer, «
Nonequilibrium Thermodynamics and the Stability
of States Far from Equilibrium,» Accounts
of Chemical Research 12 (1979), 243 - 49; Richard M. Noyes, «Oscillations in Homogeneous Systems,» Ber.
In a new dissipative structure (either a steady state or a limit cycle), concentrations
of chemicals and rates
of mass - transfer between the system and surroundings will not be those characteristic
of the previous equilibrium state (or the
nonequilibrium steady state that corresponds to it under conditions
of instability) but rather they will be the (perhaps quite different) average values which pertain to the new structure.
We have directly determined the structural dynamics
of such a
nonequilibrium phase transition in a cuprate superconductor.
Nonequilibrium phase transitions, which are defined by the formation
of macroscopic transient domains, are optically dark and can not be observed through conventional temperature - or pressure - change studies.
They presented the intrinsic molecular characteristics
of the slip phenomena by using atomistic
nonequilibrium molecular dynamics simulations
of polyethylene melts under shear flow.
These
nonequilibrium structural features are correlated with the direction
of change from sp2 [two - dimensional (2D) graphene] to sp3 (3D - diamond) electronic hybridization, and the results are compared with theoretical charge - density calculations.
Both lowering
of the activation free energy and changes in the generalized transmission coefficient (recrossing
of the transition state, tunneling, and
nonequilibrium contributions) can play a role.
Abstract: We investigate
nonequilibrium behavior in (1 +1)- dimensional stochastic field theories in the context
of Ginzburg - Landau models at varying cooling rates.
See Curry post on «
Nonequilibrium thermodynamics and maximum entropy production in the Earth system» paper by Axel Kleidon (downloadable) https://judithcurry.com/2012/01/10/
nonequilibrium-thermodynamics-and-maximum-entropy-production-in-the-earth-system/ «The Earth system is maintained in a unique state far from thermodynamic equilibrium, as, for instance, reflected in the high concentration
of reactive oxygen in the atmosphere.
Nonskeptical Elevator Summary: «Solar heating
of the Earth's surface + GHG heat radiation sustains the nonisothermal /
nonequilibrium profile
of the Earth's atmosphere.»
Alternative (skeptical) Elevator Summary: «Solar heating
of the Earth's surface + day - night surface temperature cycling sustains the nonisothermal /
nonequilibrium profile
of the Earth's atmosphere.»
The nemesis
of inductive reasoning is the prevalence in the real world
of chaotic nonlinear and
nonequilibrium pattern due to complexity and the universality
of feedbacks.
The issue
of feedbacks is raised but trying to understand feedbacks in climate without a framework
of a nonlinear /
nonequilibrium dynamic system is like trying to understand chemistry without the periodic table.