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Chapter 6: Matter far from Equilibrium
Sidebar 1
12
3 45
2
5
A. Points at Issue, Targets for Progress
B. The Limit - Equilibrium
C. The Challenge – Non-equilibrium
D. The Fundamental Challenges:
• appropriate (drastically) reduced variables (1023 few)• Link up concepts for a broad range of length scales • nonlinear structures and behaviors • emergent properties• inputs of new fluxes • emergence, amplification, selection , combinatorics, complexity, feedback and- eventually- consciousness and life itself
Side bar
Glass Sculpture (1) is one of many forms of art that rely on non equilibrium. The glass is a supercooled liquid, relaxing on many differing timescales, approaching equilibrium but never attaining it.
Beluzhov/Zhabotinsky oscillating chemical reaction (2). These spatial patterns are observed when the initially-mixed chemical reagents diffuse to form patterns (without stirring). Other similar patterns (in space and in time) are observed in many systems whose dynamical equations are nonlinear.
DySA is Nature’s preferred way of building its animate creations on various length scales:
Left: fluorescently labeledmicrotubules in a cell confined to a 40 µm triangle on a SAM-patterned surface of gold;
Middle: Fractal bacterial colony;
Right: School of fish.
10-5 M 10-1 M 10 M
Magnetohydrodynamic DySA – What is minimized? Above, two magnetic particles rotate at the interface due to a rotating magnet. They reach a nonequilibrium steady state (right), at which the magnetic force is balanced by the pairwise hydrodynamic repulsion between vortices created by the particles. This simple system combines a conservative confining potential with dissipative, hydrodynamic interactions. Is there an extremum principle that describes this “constrained” nonequilibrium steady state? Scale bars are 2 mm.
Equilibrium Non-equilibrium
Heat
Energy
5 mm
Model DySA. Above: At equilibrium, a collection of millimeter-sized magnetic particles float on a liquid-air interface in a “clump.” If one supplies energy by rotating a magnet below, the particles assemble spontaneously into an ordered array.
Below: Hydrogel particles doped with camphor floating at a water-air interface mimic chemotactic bacteria, responding to chemical gradients which they also emit. At high densities, particles organize into a lattice due to repulsive interactions.
Quorum Sensing. Colonies of the bacterium Panibacillus dendritiformis organize themselves into extravagant formations to maximize their food intake in a given environment. How?
10-3 cm
An Icelandic poppy (12) is an example of circadian rhythms - systemsthat use external energy inputs (in this case sunlight) to drive themthrough cyclic behaviors, as the rose closes at night and opens in the sunlight.
Peyton Manning (13) is a highly non-equilibrium system, that uses energy inputs to perform useful work, by processes whose efficiency is difficult to characterize, and whose functioning depends on non-equilibrium at many levels. Such self-organizing complexity is perhaps the ultimate challenge to our understanding of non-equilibrium systems.
A. Points at Issue, Targets for Progress
B. The Limit - Equilibrium
C. The Challenge – Non-equilibrium
D. The Fundamental Challenges:
• appropriate (drastically) reduced variables (1023 few)• Link up concepts for a broad range of length scales • nonlinear structures and behaviors • emergent properties• inputs of new fluxes • emergence, amplification, selection , combinatorics, complexity, feedback and- eventually- consciousness and life itself
A simple example: the molecular transport junction.
Molecular junction.
Simple example – Molecular Transport Junctions
Sketches and images of junctions in which single molecules
act as conductors, in a highly non-equilibrium situation.
bbbb
Coulomb blockade (long wire)
Kondo resonance (short wire)
E. Some Specifics, and Some Accomplishments
F. The Science of Life
G. Fluctuations
H. Design approaches- complexity, communications, and robustness.
I. Exploring Rough Landscapes – Finding Home in the Mountains, on a Dark Night
J. No Room at the Inn- Jamming Processes
Final comments
Some Successes (big to small)
Stellar evolution
Structure and dynamics of the atmosphere
Ocean currents/marine systems
Arrested relaxation (glasses, etc.)
Steady-state in gradients
Energy-pumped systems (stirred, dynamical self-assembly)
Chemical reactions
Nanoscale phenomena (finite-size effects, single-event statistics, assembly)
Biological situations
E. Some Specifics, and Some Accomplishments
F. The Science of Life
G. Fluctuations
H. Design approaches- complexity, communications, and robustness.
I. Exploring Rough Landscapes – Finding Home in the Mountains, on a Dark Night
J. No Room at the Inn- Jamming Processes
Final comments
Sidebar 2
F. The Science of Life
G. Fluctuations
H. Design approaches- complexity, communications, and robustness.
I. Exploring Rough Landscapes – Finding Home in the Mountains, on a Dark Night
J. No Room at the Inn- Jamming Processes
Final comments
Sidebar 3
Experimental progress in testing fluctuation theorems Recent developments towards a unified treatment of fluctuations in small systems are
embodied in fluctuation theorems. Fluctuation theorems (FT) relate the probabilities for a system to exchange certain amounts of energy with the thermal bath. Experimental techniques such as optical tweezers and atomic force microscopy have recently allowed scientists to directly test the validity of several fluctuation theorems.
In 2002, the group of Denis Evans in Australia verified a FT by repeatedly dragging microscopic beads through water with an optical trap, and computing the entropy production for each bead trajectory. Most notably, they occasionally observed entropy consuming trajectories. Unlike bulk systems, small systems can temporarily borrow energy from the thermal bath and use it to reduce their entropy. Of course, on average, the entropy of the system increases according to the Second Law.
There are several fluctuation theorems, each applicable to slightly different thermodynamic systems. The Crooks fluctuation theorem and the closely related Jarzynski equality
are directly applicable to mechanically perturbed small systems such as RNA hairpins or single proteins.
The Jarzynski equality asserts something remarkable. If you take a small system and drive it many times from state A to state B, then if you perform a particular kind of averaging over those trajectories you can recover the free energy difference between A and B, regardless of the details of the system and how violently it is perturbed. The Jarzynski equality is particularity beautiful when written in terms of the dissipated work, as shown here: the Boltzmann-weighted average over dissipated works always equals unity. Like other fluctuation theorems and closely related results, the Jarzynski equality relates equilibrium thermodynamics with non-equilibrium thermodynamics: it is a bridge between those two fields.
The JE has been tested by mechanically stretching a single molecule of RNA, a non-harmonic dissipative system, reversibly and irreversibly, between its folded and unfolded conformations. Depending on how rapidly the hairpin was unfolded, different amounts of work were needed. When the polymer was unfolded slowly, the average forward and reverse trajectories could be super-imposed, indicating a reversible reaction. When the polymer was unfolded more rapidly, the mean unfolding force increased. The folding/unfolding cycle was thus hysteretic, indicating the dissipation of work. Application of the JE to the irreversible work trajectories yielded an excellent estimate of the free energy of unfolding process.
Fluctuation theorems are not only tools that experimentalists can use to extract equilibrium information from non-equilibrium experiments, but are also useful to simulate the properties of non-equilibrium systems and may ultimately guide the design of such systems.
MOLECULAR MACHINES
F. The Science of Life
G. Fluctuations
H. Design approaches- complexity, communications, and robustness.
I. Exploring Rough Landscapes – Finding Home in the Mountains, on a Dark Night
J. No Room at the Inn- Jamming Processes
Final comments
hurricane from space station ( from wikipedia)
F. The Science of Life
G. Fluctuations
H. Design approaches- complexity, communications, and robustness.
I. Exploring Rough Landscapes – Finding Home in the Mountains, on a Dark Night
J. No Room at the Inn- Jamming Processes
Final comments
Picture 6 azo benzene isomerization
Picture 4
Picture 5
F. The Science of Life
G. Fluctuations
H. Design approaches- complexity, communications, and robustness.
I. Exploring Rough Landscapes – Finding Home in the Mountains, on a Dark Night
J. No Room at the Inn- Jamming Processes
Final comments
Picture 7
F. The Science of Life
G. Fluctuations
H. Design approaches- complexity, communications, and robustness.
I. Exploring Rough Landscapes – Finding Home in the Mountains, on a Dark Night
J. No Room at the Inn- Jamming Processes
Final comments
Many of the processes that characterize energy flow, capture, production, storage and transduction occur far from equilibrium; so do most significant biological behaviors, and important processes in molecules, solids, oceans and atmospheres.
Since most current understanding of physical and biological systems is based on equilibrium concepts, far-from-equilibrium behaviors are intrinsically and crucially significant. The combination of significance and energy relevance, of intrinsic scientific knowledge and its application, characterize the Grand Challenge of systemsfar from equilibrium. Progress in understanding and quantifying these behaviors must be made, to deal effectively with the energy, climate, materials, biological and security issues facing humankind.
Things we would like to do:
Experimentally characterize, and formally understand, pathways in non-equilibrium processes?
optical tweezers, atom traps, synthetic nanomachines, biological molecular machines, and related structures.
New thermodynamic type formalisms, (Jarzynski relationship, Crooks’ theorem), for non-equilibrium work
New simulation techniques: transition path sampling, distorted landscape pictures,…
“Monte Carlo” approaches - agent-based and evolutionary algorithms, cluster movement Monte Carlo, for nanoscale non- equilibrium growth, pattern formation.
Where we are, and where we might go
Some Questions:
• In transport junction behavior, how does the non-equilibrium process interact with the phenomenon of strong correlation?
• Can we change the processes of cell trafficking by simple nanoparticle addition, affecting the geometry of the environment and reorganizing cell trafficking modes?
• To what extent do thermal emission point sources such as factories or nuclear power plants modify the microclimate down wind – could other, better dissipation schemes be found that could alleviate these effects?
• Can we understand enough about biological repair mechanisms to use them in molecular and solid state device applications – that is, can we make a self repairing computer? Or a self repairing transistor? Or a self repairing lighting? Or self repairing solar cells?
• Can we understand the function of so-called vectorial processes in biology, something as straightforward as kinesin/actin motions or active transport within cells, well enough to mimic them with artificial systems?
• Can we control of geometry at the nanoscale, to influence or direct structures and processes – that is, can we do chemistry in a nanobox, where the processes and products are controlled by the nature of the box?
• Can we develop efficiency measures or artificial cellular processes, •and for highly non-equilibrium processes, to replace the Carnot efficiencies of equilibrium systems?
• Can we use the multiple temperature phenomena, associated with very slow relaxations of particular subsets of modes, for thermal control? Can we utilize artificial structures to store excitations long enough for energy transduction from the vibrational manifold into the electronic, and thereby to increase efficiency of solar capture devices?
• Can we understand the nature of fluctuations in non-equilibrium situations?
• Can we comprehend how systems search free energy landscapes? What determines the nature of molecular recognition, from nanostructures to kinetics to biomolecular structure building?
• Can we characterize systems with "jamming", (nonstandard constraints) in concentrated suspensions, foams, glasses? How can we know when these systems have phase transitions (some do, some don’t)?
• Single molecule dynamical experiments observe the time trace of a single molecule. Many (more than expected) show long time tails suggesting very long microscopic relaxation time scales. Some of these are nanoparticles, some are single enzyme molecules. How can we deal with this, and what general rules apply?
• Fluctuations change away from equilibrium, and some chemical motors seem to act like Maxwell’s demon. What can be said about these fluctuations? Experimental characterization of how different sorts of nonequilibrium yield different fluctuation patterns. Coupling of external entities (motors, etc.)
• Can we comprehend how systems search free energy landscapes? What determines the nature of molecular recognition, from nanostructures to kinetics to biomolecular structure building?
• Can we characterize and perform calculations in systems with "jamming", (nonstandard constraints) in concentrated suspensions, foams, glasses? How can we know when these systems have phase transitions (some do, some don’t)?
• With the advent of single molecule dynamical experiments, we can now observe the time trace of a single molecule and compare this to the predictions of ensemble statistical mechanics. Many (more than we had expected) show long time tails suggesting that these systems have microscopic relaxation time scales that are very long. Some of these are nanoparticles, some are single enzyme molecules. How can we deal with this, and what general rules apply?
Picture 3
