{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:32:18Z","timestamp":1760243538662,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2012,2,17]],"date-time":"2012-02-17T00:00:00Z","timestamp":1329436800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>I defend the idea that the fact that no system is entirely isolated (\u201cInterventionism\u201d) can be used to explain the successful use of the microcanonical distribution in statistical mechanics. The argument turns on claims about what is needed for an adequate explanation of this fact: I argue in particular that various competing explanations do not meet reasonable conditions of adequacy, and that the most striking lacuna in Interventionism\u2014its failure to explain the \u201carrow of time\u201d\u2014is no real defect.<\/jats:p>","DOI":"10.3390\/e14020344","type":"journal-article","created":{"date-parts":[[2012,2,17]],"date-time":"2012-02-17T11:01:05Z","timestamp":1329476465000},"page":"344-369","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interventionism in Statistical Mechanics"],"prefix":"10.3390","volume":"14","author":[{"given":"Stephen","family":"Leeds","sequence":"first","affiliation":[{"name":"Department of Philosophy, University of Wisconsin, Curtin Hall, 3243 N. Downer Avenue, Milwaukee, WI 53211, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Albert, D.Z. (2000). Time and Chance, Harvard University Press.","DOI":"10.4159\/9780674020139"},{"key":"ref_2","unstructured":"See [1], p. 132. The text reads \u201cmacroscopic two-body systems\u201d, reflecting Albert\u2019s having chosen to discuss the approach to equilibrium in terms of the equalization of temperature between two bodies in thermal contact. His point applies to systems in general."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1023\/A:1018870725369","article-title":"The spin-echo experiments and the 2nd law of thermodynamics","volume":"28","author":"Ridderbos","year":"1998","journal-title":"Found. Phys."},{"key":"ref_4","first-page":"399","article-title":"The \u201cPast Hypothesis\u201d: Not even false","volume":"37","author":"Earman","year":"2006","journal-title":"Stud. Hist. Philos. Sci."},{"key":"ref_5","unstructured":"Since Albert is about to appear in connection with a quite different picture, I will refer to the other one, when we get to it, as Albert\u2019s account, and call this one the GRW account. In fact, Albert\u2019s name really belongs on the GRW account, since (at least so far as I know) no one before him had the nice idea of using GRW to explain the approach to equilibrium; the account I will be calling Albert\u2019s is in fact one that has been proposed by several people."},{"key":"ref_6","unstructured":"In what follows, I switch often, and without notice, between talking about measures and talking about distributions. In general, if I refer to a certain measure \u03bc* as X-measure (e.g., mc-measure), then I am always supposing that \u03bc* can be given by a density function f with respect to Lebesgue measure; I will then refer to f as the X-distribution."},{"key":"ref_7","unstructured":"It is worth noting that at one point Albert himself invokes external perturbations. See [1] p. 158."},{"key":"ref_8","unstructured":"If we take \u03bc to be the microcanonical distribution, then \u03bc has the important merit of being an extremely natural distribution\u2014though we might recall that it was not Boltzmann\u2019s first choice. Important as it is, this fact cannot be the (C) we seek: it is just one more purely logical consequence of H&M&D. Where the naturalness of some proposed \u03bc might play a role is as a reason to think that that distribution is a match to the empirical frequencies\u2014though, as we are about to see, there are difficulties in making this claim about the microcanonical distribution."},{"key":"ref_9","unstructured":"Here are some other cases where we would reject a proposed explanation for similar reasons. \u201cAll particles that are not neutrinos obey rule X\u201d is unacceptable as a fundamental law, not because it is not universal\u2014it can obviously be written as a universally quantified conditional\u2014but because it immediately invites the question \u201cWhy not neutrinos?\u201d Similarly, a proposal that the chance of some process is x can be cast into serious doubt by showing that in a specific kind of situation, the predicted statistics are invariably violated, so long as there are a reasonably large number\u2014say 500\u2014of instances of such situations. This is the case even if overall the statistics are an excellent match to the predictions\u2014which of course can happen if there are many more than 500 cases overall."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1093\/bjps\/53.1.83","article-title":"Boltzmann\u2019s time bomb","volume":"53","author":"Price","year":"2002","journal-title":"Br. J. Philos. Sci."},{"key":"ref_11","unstructured":"I have been able to find one passage, but only one, in which Price might be interpreted as subscribing to the view that the mc*-distribution matches the statistics, namely in Section 3.2 of [20]."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1086\/423749","article-title":"Can conditioning on the \u201cPast Hypothesis\u201d militate against the reversibility objections?","volume":"71","author":"Winsberg","year":"2004","journal-title":"Philos. Sci."},{"key":"ref_13","unstructured":"This is what I take to be the core of Winsberg\u2019s argument. Winsberg\u2019s own statement places a great deal of emphasis on the claim that contact with the outside world effectively \u201crerandomizes\u201d the state of the glass of water. Such a claim is no part of the argument as I present it."},{"key":"ref_14","unstructured":"Or can we say that, given that the region of phase space in which the ice-water is fated to melt is enormous, it would be discrepant for the world to occupy a phase point outside this region? But then the empirical distribution is discrepant with the mc* distribution no matter what, since every phase point lies outside an uncountable infinity of large regions."},{"key":"ref_15","unstructured":"On the phase spaces of individual macroscopic systems\u2014so this idea requires one to reject Winsberg\u2019s argument that the mc*-distribution is just the mc-distribution."},{"key":"ref_16","unstructured":"There is another, vague, argument for the claim which I have not seen in print, but which may be at the back of people\u2019s minds. This is the idea that since the mc*-distribution is just a conditionalized mc-distribution, we have reason to suppose that when we update it and conditionalize over the macrostate of the world today, what we get is more or less a product of mc-distributions over the current macrostates of the various systems that make up our world. If this were so, then since mc-most glasses of ice-water will melt at the right rate, it will also be the case that mc*-most initial states that involve a glass of ice-water here and now will be states in which the ice melts at the right rate. But why believe this? The current distribution doesn\u2019t factor into a product; indeed it exhibits strong correlations among the components: run backward, a glass of water will merge with all the other water in the city reservoir and so on back in just the way needed to bring about the low-entropy initial macrostate. The marginals of the current distribution on the subsystems may or may not resemble the mc-distribution in the ways we need, but I don\u2019t know how one could argue for this without delving more deeply\u2014much more deeply\u2014into the dynamical details"},{"key":"ref_17","unstructured":"Likewise, ergodic approaches to foundations certainly have their problems, but it seems unreasonable to object to the modern, post-Birkhoff version of such approaches on the grounds that they do not derive their central statistical claim (that the phase point on a system can be expected to be on an ergodic trajectory) from initial conditions."},{"key":"ref_18","unstructured":"Note that in addition there is a sense in which Interventionism invokes less explanatory apparatus than do appeals to distributions over the initial state. The latter connect the favored distribution with the phenomena only via the assumption that the one and only initial state of the world falls into a particular typical subset (of course it cannot fall into all typical subsets); Interventionism requires no such intermediate step."},{"key":"ref_19","unstructured":"See [3], p. 1267."},{"key":"ref_20","unstructured":"Callender, C. (2002). Burbury\u2019s Last Case: The Mystery of the Entropic Arrow, Cambridge University Press."},{"key":"ref_21","unstructured":"Call a state p an m-type state, for m = 1,\u20266, if p\u2019s lower entropy neighbor is at position m. Then one might make the conditional probability of the die rolling m, given that it was followed by an m-type state, to be 5\/6, while allowing the conditional probability of rolling m to be 1\/6, given any preceding state."},{"key":"ref_22","unstructured":"I should perhaps repeat that our assumption that there is a single distribution D governing the interventions is an over-simplification. Given a fixed characterization of the system on which the interventions and IIF\u2019s are acting, to propose a single D for the interventions such that the time reversal D* of D governs the IIFs requires substantial assumptions either about symmetry properties of D, or of the distribution of states of the system, or both. I want to avoid both kinds of assumptions (especially the second). It would be even more to ask that our D and D* be appropriately related, whatever system they are acting on. This is one reason why I think we should postulate not a single distribution but a family of such: we achieve neutrality about time-direction by requiring that the family of distributions governing the IIF\u2019s consists of the time reversals of those governing the forward interventions. I expect this requirement will be easy to meet if we are willing to accept a rather broad family of appropriate distributions. It might be that the distribution Y of IIF\u2019s on a particular system might be quite different from the time reversal of the distribution X of interventions on that systems, and yet each conform quite well to our intuitive idea of \u201crandom influences from outside\u201d. It might be clearer to read D and D* in the text as X and Y, and drop the idea that one is the time-reversal of the other."},{"key":"ref_23","unstructured":"What about the idea that if we move to the joint phase space of systems and IIF\u2019s, we can set things up so that the conditional probability is high, for a system in state p, that the IIF\u2019s will be such as to drive it backwards towards lower entropy? I distinguish this from the undoubted fact that the actual IIF\u2019s do in fact generally turn out to be exactly such as to drive the systems on which they intervene backward toward lower entropy. Of course this is true (and interventionism offers an explanation of why it is true); what the present idea requires, however, is that we accept the existence of correlations between systems and IIF\u2019s as the brute statistical fact that is going to explain all the rest. I have been urging that the only statistical facts qualified to play this role have to be in some way natural; it is hard however to see how any reasonably natural joint distribution over systems and IIF\u2019s could make probable the correlations that are needed. For p a phase point of a system, let Ap be the set of IIF\u2019s guaranteed to send a system in state p towards lower entropy, in the reverse time direction, for the next small interval of time. With P as our joint probability, notice that for any fixed p*, P(Ap*|p) must be high when p = p* and fall off rapidly as p moves away from p*: this follows from the fact that Ap and Ap* are quite different, even when p is quite close to p*, together with the assumption, needed for the correlations, that most of the weight of P( |p) is concentrated on Ap. Likewise, and for the same reasons, P( |p*) varies, by any natural measure, rapidly over intervention phase space. It is hard to see what kind of natural distribution could meet this requirement."},{"key":"ref_24","unstructured":"Even if some version of implicit order gave us what we wanted, there would still be the following difficulty. For any real case of implicit order I can think of, e.g., the correlations between what is going on on your TV and mine during the World Cup, we expect to be able to explain it in terms of dynamical and statistical mechanical principles: more generally, it is reasonable to suppose that we can explain why implicit order arises, in terms of the initial macrostate evolving along a path that is probable according to mc. But if our entire explanation for the fact that entropy decreases away from Df is that the world started in Di and followed a P-probable path, which produced implicit order in Df, which made backwards decrease in entropy from Df improbable, then the explanation seems redundant: we\u2019ve already explained why entropy decreased away from Df before we mentioned implicit order."},{"key":"ref_25","unstructured":"Thus, if our distributions are of the form p(v, x,y,z), giving the probability that a particle of velocity v will appear at x,y,z in the next second, then they will neither demand nor forbid correlations between the velocities or locations of distinct particles."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1086\/367873","article-title":"Foundations of statistical mechanics: Two approaches","volume":"70","author":"Leeds","year":"2003","journal-title":"Philosophy Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/S1355-2198(01)00028-4","article-title":"Determinism and chance","volume":"32B","author":"Loewer","year":"2001","journal-title":"Stud. Hist. Philos. Mod. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1086\/587821","article-title":"The justification of probability measures in statistical mechanics","volume":"75","author":"Davey","year":"2008","journal-title":"Philos. Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/2\/344\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:57Z","timestamp":1760219337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/2\/344"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,17]]},"references-count":28,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,2]]}},"alternative-id":["e14020344"],"URL":"https:\/\/doi.org\/10.3390\/e14020344","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,2,17]]}}}