Menon In Addition To Callender On The Physics Of Stage Transitions

In an before transportation service I considered the topic of stage transitions equally a possible source of emergent phenomena ( link ). I...

In an before transportation service I considered the topic of stage transitions equally a possible source of emergent phenomena (link). I argued at that spot that stage transitions are indeed interesting, but don't heighten a serious occupation of strong emergence. Tarun Menon considers this number inwards substantial exceptional inwards the chapter he co-authored alongside Craig Callender in The Oxford Handbook of Philosophy of Physics, "Turn together with confront the foreign ... ch-ch-changes: Philosophical questions raised past times stage transitions" (link). Menon together with Callender render a real careful together with logical concern human relationship of 3 ways of approaching the physics of stage transitions inside physics together with 3 versions of emergence (conceptual, explanatory, ontological). The slice is technical but real interesting, alongside a somewhat deflating decision (if you lot are a fan of emergence):

We accept found that when i clarifies concepts together with digs into the details, alongside honor to criterion textbook statistical mechanics, stage transitions are best thought of equally conceptually novel, but non ontologically or explanatorily irreducible. 

Menon together with Callendar review 3 approaches to the phenomenon of stage transition offered past times physics: classical thermodynamics, statistical mechanics, together with renormalization grouping theory. Thermodynamics describes the conduct of materials (gases, liquids, together with solids) at the macro level; together with statistical mechanics together with renormalization grouping theory are theories of the micro states of materials intended to permit derivation of the macro conduct of the materials from statistical properties of the micro states. They depict this human relationship inwards these terms:

Statistical mechanics is the theory that applies probability theory to the microscopic degrees of liberty of a organization inwards companionship to explicate its macroscopic behavior. The tools of statistical mechanics accept been extremely successful inwards explaining a number of thermodynamic phenomena, but it turned out to hold out peculiarly hard to apply the theory to the report of stage transitions. (193)

Here is the mathematical Definition of stage transition that they provide:

Mathematically, stage transitions are represented past times nonanalyticities or singularities inwards a thermodynamic potential. H5N1 singularity is a betoken at which the potential is non infinitely differentiable, thence at a stage transition around derivative of the thermo­dynamic potential changes discontinuously. (191)

And they offering this definition:

(Def 1) An equilibrium stage transition is a nonanalyticity inwards the gratuitous energy. (194)

Here is their description of how the renormalization grouping theory works:

To explicate the method, nosotros render to our stalwart Ising model. Suppose nosotros coarse­grain a 2­D Ising model past times replacing 3 × 3 blocks of spins alongside a unmarried spin pointing inwards the same administration equally the bulk inwards the master copy block. This gives us a novel Ising organization alongside a longer distance betwixt lattice sites, together with peradventure a unlike coupling strength. You could expect at this coarse­graining physical care for equally a transformation inwards the Hamiltonian describing the system. Since the Hamiltonian is characterized past times the coupling strength, nosotros tin also depict the coarse­graining equally a transformation inwards the coupling parameter. Let K hold out the coupling forcefulness of the master copy organization together with R hold out the relevant transformation. The novel coupling forcefulness is K′ = RK. This coarse­graining physical care for could hold out iterated, producing a sequence of coupling parameters, each related to the previous i past times the transformation R. The transformation defines a menstruum on parameter space. (195)

Renormalization grouping theory, then, is essentially the mathematical ground of coarse-graining analysis (link).

The key difficulty that has been used to Earth arguments well-nigh strong emergence of stage transitions is at nowadays apparent: at that spot seems to hold out a logical disjunction betwixt the resources of statistical mechanics together with the findings of thermodynamics. In theory physicists would similar to agree that statistical mechanics provides the micro-level representation of the phenomena described past times thermodynamics; or inwards other words, that thermodynamic facts tin hold out reduced to derivations from statistical mechanics. However, the Definition of a stage transition inwards a higher house specifies that the phenomena display "nonanalyticities" -- instantaneous together with discontinuous changes of state. It is easily demonstrated that the equations used inwards statistical mechanics create non display nonanalyticities; modify may hold out abrupt, but it is non discontinuous, together with the equations are infinitely differentiable. So if stage transitions are points of nonanalyticity, together with statistical mechanics does non acknowledge of nonanalytic equations, together with thence it would seem that thermodynamics is non derivable from statistical mechanics. Similar reasoning applies to renormalization grouping theory.

This occupation was solved inside statistical mechanics past times admitting of infinitely many bodies inside the organization that is represented (or alternatively, admitting of infinitely compressed volumes of bodies); but neither of these assumptions of infinity is realistic of the cloth world.

So are stage transitions "emergent" phenomena inwards either a weak feel or a strong sense, relative to the micro-states of the cloth inwards question? The strongest feel of emergence is what Menon together with Callender telephone telephone ontological irreducibility.

Ontological irreducibility involves a real strong failure of reduction, together with if whatever phenomenon deserves to hold out called emergent, it is i whose description is ontologically irreducible to whatever theory of its parts. Batterman argues that stage transitions are emergent inwards this feel (Batterman 2005). It is non just that nosotros create non know of an adequate statistical mechanical concern human relationship of them, nosotros cannot educate such an account. Phase transitions, according to this view, are cases of genuine physical discontinuities. (215)

The possibility that stage transitions are ontologically emergent at the storey of thermodynamics is raised past times the betoken well-nigh the mathematical characteristics of the equations that constitute the statistical mechanics description of the micro storey -- the infinite differentiability of those equations. But Menon together with Callender give a compelling ground for thinking this is misleading. They believe that stage transitions constitute a conceptual novelty alongside honor to the resources of statistical mechanics -- stage transitions create non fit to natural kinds at the storey of the micro-constitution of the material. But they debate that this does non constitute that the phenomena cannot hold out explained or derived from a micro-level description. So stage transitions are non emergent according to the explanatory or ontological understandings of that idea.

The nub of the number comes downward to how nosotros construe the idealization of statistical mechanics that assumes that a cloth consists of an infinite number of elements. This is apparently untrue of whatever existent organization (gas, liquid, or solid). The fact that at that spot are boundaries implies that of import thermodynamic properties are non "extensive" alongside volume: twice the mass leads to twice the entropy. But the agency inwards which the finitude of a mass of cloth affects its conduct is through the effects of novel behaviors at the edges of the volume. And inwards many instances these effects are pocket-sized relative to the conduct of the whole, if the mass is large enough.

Does this fact imply that at that spot is a neat mystery well-nigh extensivity, that extensivity is genuinely emergent, that thermodynamics does non trim to finite northward statistical mechanics? We advise that on whatever reasonably uncontentious agency of defining these terms, the respond is no. We know precisely what is happening here. Just equally the minute police draw of thermodynamics is no longer strict when nosotros become to the microlevel, neither is the concept of extensivity. (201-202)

There is an of import idealization on the thermodynamic description equally good -- the notion that several specific kinds of changes are instantaneous or discontinuous. But this supposition tin also hold out seen equally an idealization, corresponding to a physical organization that is undergoing changes at unlike rates nether unlike environmental conditions. What thermodynamics describes equally an instantaneous modify from liquid to gas may hold out meliorate understood equally a rapid physical care for of modify at the tooth storey which tin hold out traced through inwards a continuous way.

(The fact that around systems are coarse-grained has an interesting implication for this laid of issues (link). The interesting implication is that piece it is to a greater extent than oft than non truthful that the micro states inwards such a organization entail the macro states, the opposite is non true: nosotros cannot infer from a given macro dry ground to the exact underlying micro state. Rather, many possible micro states fit to a given macro state.)

The decision they make is worth quoting:

Phase transitions are an of import instance of putatively emergent behavior. Unlike many things claimed emergent past times philosophers (e.g., tables together with chairs), the alleged emergence of stage transitions stems from both philosophical together with scientific arguments. Here nosotros accept focused on the instance for emergence built from physics. We accept found that when i clarifies concepts together with digs into the details, alongside honor to criterion textbook statistical mechanics, stage transitions are best thought of equally conceptually novel, but non ontologically or explanatorily irreducible. And if i goes past times textbook statistical mechanics, together with thence an declaration tin hold out made that they are non fifty-fifty conceptually novel. In the instance of renormalization grouping theory, consideration of infinite systems together with their singular conduct provides a primal theoretical tool, but this is compatible alongside an explanatory reduction. Phase transitions may hold out “emergent” inwards around feel of this protean term, but non inwards a feel that is incompatible alongside the reductionist projection broadly construed. (222)

Or inwards other words, Menon together with Callender refute i of the most technically compelling interpretations of ontological emergence inwards physical systems. They demo that the phenomena of stage transitions equally described past times classical thermodynamics are compatible alongside existence reduced to the dynamics of private elements at the micro-level, thence stage transitions are non ontologically emergent.

Are these arguments relevant inwards whatever agency to debates well-nigh emergence inwards social organization dynamics? The at nowadays relevance is limited, since these arguments depend alone on the mathematical properties of the ways inwards which the micro-level of physical systems are characterized (statistical mechanics). But the to a greater extent than full general lesson does inwards fact seem relevant: rather than just postulating that certainly social characteristics are ontologically emergent relative to the actors that brand them up, nosotros would hold out meliorate advised to expect for the local-level processes that human activeness to convey well-nigh surprising transitions at critical points (for example, the shift inwards a flock of birds from random flying to a swarm inwards a few seconds).