Jo, thanks for the reply and the set of good questions. I'll respond to them in reverse order the best I can.

> My suspicion is that most definitions in this area, despite being 'broadly used' are likely to be highly problematic in rigorous thermodynamics terms, and probably in metaphysical terms for that matter! Buzz words tend to buzz more than do work.

I agree, and so I try to be precise, but my brevity and the jargon may have mislead.

> I am a bit puzzled by the reference to energy dissipation.

"Energy dissipation" may sound like a buzz word, but it addresses that references to free energy seem to beg the question. Like infinite regress in causal chains, a reference to free energy (or causal power) seems to imply a physical or conceptual frame within which a process makes sense in its own terms but does not make sense when the frame is enlarged. Why do we presume and how do we explain the presence of this free energy? Here I resort to what I hope is a sound thermodynamic principle: a thermodynamic engine is the relation of an actual and a possible more probable state of affairs, and it is the ultimate engine of all change. I'd appreciate your criticism of this argument. In your glacier example, it would be the dissipation of gravitational energy to the more probable form of energy, heat.

I spoke of "energy dissipation" in order to avoid contention. Actually, I see energy and structure as equivalent and so prefer speaking of the dissipation of a "probability gradient". There are standard accounts that appeal to an energy gradient (Stuard Kaufmann for example) and which refer to a tradient between order and chaos (Atkins on entropy, for example). In the burning of fuel, the energie dormant in internal molecular bonds is released as Gibbs free energy, as heat that does work. But also the  improbable structures of complex hydrocarbon molecules dissipate into simpler and more probable molecules of water, carbon monoxide, etc. This can be adequately described in terms of either energy or structure, and so I use what they have in common: relative probability. What  is your reaction to this? There are some esoteric philosophical issues here, such as any structure being improbable in principle because has more information than its constituents and how these improbable bonds were created in the first place by a dissipation of solar energy,

> What about a glacier? The more it accumulates mass of snow the faster it falls off the mountain so its size remains roughly constant (as does its ability to accumulate snow).

Thanks for the interesting example, but I'm not sure of it. I'm thinking here of Heraclitus' paradox about stepping a second time in the same river. I suspect that unless one adopts a rather strained philosophical notion of identity rather than a physical definition as a state of affairs, it is not the same glacier that keeps its size, but a new state of affairs that shares many properties with an old state of affairs. Although your example is appreciated, I'm not entirely comfortable with it.

> I guess the question is why this matters to philosophy. Are homeostatic systems to be attributed some sort of magical animistic property? Are 'systems' anything more than a heuristic category for chunking ideas anyway?
 
I leave the most difficult questions to last. One of your questions might be: Why does philosophy matter to science, rather than science to philosophy? This could raise all kinds of issues, but I respond to your rhetorical question by offering at least one possible answer. I see science as a species of action, and philosophy as a species of thought. That they interact in important ways is beside the point. The former engages the world in physical terms; the latter engages culture in mental terms. Putting aside the ambiguities in what is known as scientific realism, because I make action foundational in human life, I see philosophy as only a tool to help us construct knowledge that arises from our active engagement with the world and to represent that experience in thought and communications. Critical empiricists and I'm sure many other philosophers would disagree, of course, but I suspect most scientists would find the point congenial. I don't think the issue can be resolved without transcending the categories by which it is defined, and otherwise it comes down to whether there is justification for making action foundational. To address this would require a different thread.

Then you raise an even more challenging question regarding vitalism and system. A "system" seems to imply a physical or conceptual closure, and so is necessarily a one-sided view of things. A more accurate term would be "level", for this word implies a relation with what is not intrinsic (or observable) to a system. Nevertheless, the concept system seems to have utility. In practical terms, the more you close a system physically and conceptually, the more is causal determinism unequivocal and outcomes predictable (I assume that absolute closure is a hypothetical limiting case and that all systems are in principle open to some degree). In daily life or in the scientific laboratory, it is useful to create or presume closure because one wants outcomes to be relatively predictable. For this reason, deductive logic is an effect of conceptual closure and does not seem true of the actual world in which we live or the world of mental life, where unpredictability is perhaps more characteristic than predictability (and this is the concern of what are termed the historical sciences). Conventionally, "system" refers to properties that emerge from the relation of its constituents rather than from just their intrinsic properties, and these "systemic properites" are manifest either in a physical boundary or in its constituents acquiring properties that are other than intrinsic. If I understand your point correctly (of which I am not absolutely certain), I don't see why "system" should be a problematic concept. If sodium and chlorine molecules bond, it gives rise to a set of novel but predictable properites that are referred to as those of "salt", which neither molecules originally had.

Now,  how does vitalism come into this? It seems to me that if one assumes closure, a system rather than a level, any change that is not predictable based on properties intrinsic to the system's constituents becomes mysterious or at least a surprise. Usually such unpredictability is attributed to contengencies, but once contingencies are taken into account by enlarging the scope of the system, then we regain closure and near unequivocal determinism: the contingency becomes a known causal factor within the wider system. But even then, prediction is never absolute, even in quantum electrodynamics. That's why we introduce standard deviation into beginning physics courses. Another source of deviation in any real systems is the n-body problem, but I suspect this is an epistemological artifact. Finally, if we are modal realists in some sense, there are aspects of systems that are unobservable and don't reduce to empirical properties and yet have real effects. Arguably, none of these limits on predictability necessarily introduce anything supernatural. Even critical empiricists these days accept that all science engages theortical objects that are presumed to be real such as the Big Bang, black holes, and gluons, to say nothing of our conceptual frame and axioms.

I infer from open-system thermodynamics, such as the work of Prigonine, that natural systems that might be homeostatic must be open and driven by the dissipation of a probability gradient (I don't distinguish by this term an  improbable energy and improbable structure), and I understand that dissipation of improbable actuality to a more probable possible state is the ultimate engine of change. For example, the tropical cyclone and our climate are ultimately driven by a dissipation of solar energy into the more probable form of heat, and they are homeostatic for a while. I believe it is safe to say that structural constraints on the dissipation of the probability gradient (I'd argue necessarily) give rise to novel structure. I sense that if those constraining structures are the intrinsic properties of system constituents, the resulting new structure is an equilibrium system, but if intrinsic properties of constituents are overridden by the structure of an interface that constrains the dissipation of the principle probability gradient defined by the frame, the system is non-equilibrium.

I have the feeling that feedback loops are necessarily present in homeostatic (or any other regular trajectories, such as periodicity), and while they help explain the empirical specifics of a homeostatic system, they are only half the story. Let me speculate. Starting from such assumptions that a) all things are in principle processes, b) that structures constrain possible states in terms of their relative probability, it follows that in equilibrium systems its constituents enter into a relation that is probable in terms of their intrinsic properties (this is the structural theory of persistence). But when it comes to systems that are non-equilibrium, the probable relations implied by the intrinsic properties of constituents is overriden by the probability distribution defined by the structure of an interface between the system and the its principle probability gradient. This changes the probability distribution of the system. Let me explain, starting with equilibrium systems.

Because the relation of actuality and possibility is a probability distribution and most systems have more than one possible state that is relatively probable, what state it ends up in will be a function of the relative probability of these possible states. The probability distribution of most systems have several peaks representing states of relatively high probability separated by lower probability valleys. Crystal formation, is a good example, where the packing rules defined by molecular structure determine the relative probability of the possible molecular bonds and the resulting lattice structure allows one relatively probable state to prevail over others, to lock in crystal formation to just one structure rather than spawning multiple structures, the numerical distribution of which would be a function of their relative probability. If we consider a relatively closed system, this probability distribution is defined by the intrinsic properties of its constituents, and its trajectory is fairly predictable although the result is novel because the bonds of structure add information not present in each molecule. Crystal formation is exothermic and thus driven by a dissipation of a probability gradient (supersaturation, for example), but once it stops, the resultinh crystal is an internally probable structure that is improbable in relation to the world and persists independently of any dissipative process. On the other hand, if the system is open in the sense that there is a boundary structure that constrains the dissipation of the principle probability gradient defined by the frame and which changes the system's probability distribution, then the outcome that is improbable in relation to intrinsic properties must be sustained by a continuing dissipation. That's why open system thermodynamics calls such systems "dissipative systems". The interface draws upon the dissipation of the primary probability gradient to alter the probability distribution, doing the work of overriding the probable relations defined by the intrinsic properties of the constituents.

Not only do such systems result in structures that are improbable in relation to the intrinsic properties of their constuents (the more recent definition of emergence disregards novelty and limits it to improbability), but such systems can also change from one state to another. I suggest two conditions that give rise to a structural change of state: a) The probability gradient falls outside a certain range (if too high, other states become more probable and ultimately all possible states become probable and we up end back with a virtual vacuum; too low, and the structure of the non-equilibrium system collapses and ultimately all structure collapses, as in Heat Death). b) The structure that constrains the probability gradient changes sufficiently (I subsume perturbation under this situation, but that's another issue). These two conditions are ontologically inseparable, for both are relations of modalities that is anchored in actual structure, but we conceptually isolate them.

Now, how about homeostasis? If systems are probabilistic processes, their states can be described as a probability curve. This means that their structure is to some extent insulated from minor perturbations because the purturbation would necessarily moves its state to what is less probable. We see this everywhere. In crystal growth, a minor purturbation introduces a linear change in its growth trajectory, but usually its starting structure will continue. In organic systems, like a tree, it recovers from minor perbuations that don't affect the basic structure that makes it a tree. Borrowing the terminology of General Systems Theory, an "immature" incipient systems is very prone to a new trajectory because of perturbations, but a "mature" system has "locked in" to become rather insentive to perturbations and maintains its trajectory despite them. In short, the trajectory of a system depends on a combination of a) empirical specifics (intrinsic properties of constituents and for non-eqilibrium systems its interfaces) to define the quality of change and b) a probability grandient sufficient to drive change itself. 

While the persistence of structures is typical (and so forms part of the definition of "structure"), homeostasis seems to imply a feedback such that it makes a non-equilibrium system less sensitive perturbations that would otherwise change its trajectory. This is a fancy way to describe an animal in search for food. I don't take it to be unreasonable that an inorganic system might _happen_ to have a feedback loop that changes the intrinsic properties of system constituents or its interface in such a way that its probability distribution is maintained. Since feedback loops are common, I see nothing supernatural for one to happen to maintain a probability distribution despite perturbations. However, I look for a clear example that lends itself to analysis. Take an eddy in the water of a moving stream. This is a structure that arises from a boundary constraint on the dissipation of the momentum of moving water. Now, if you put your hand into the eddy, this imposes the perturbation of a new constraint. While this certainly affects the eddy locally, unless your hand is big in size and strength, the eddy remains an eddy. This seems because the boundary structure that constrains the movement of water prevails over the perturbation of your inserted hand.

So the eddy may be a homeostatic system because of three factors: a) boundary conditions define the quality of its empirical specifics, b) the constraint of these boundary conditions on the dissipation of the energy of the  flow of water offers an engine to drive it and create its probability distribution, and c) either the perturbation of your hand (its structure and your work to resist the current) does not override (a) and (b) or there _happens_ to be a feedback such that your hand changes the probability distribution in such a way that the structure of the system survives in spite of it. Given the frequency of feedback loops, it is not surprising that every once in a while one happens to support homeostasis. So I may have answered my own question, but in so doing have relied on some metaphysical and physical presumptions which may be unintelligible or problematic.

Haines Brown