Thermodynamics and Statistical Mechanics

Despre căldură, temperatură, și modalități de măsurare, și aplicații practice în inginerie. Un punct de vedere contemporan privind energia, termodinamica și legile ei, cu detalierea celor mai importante principii care o guvernează. Un capitol special este dedicat schimbărilor climatice și încălzirii globale actuale. Explicații clare ale fenomenelor, evitând formulele matematice complexe. -/- CUPRINS: -/- Căldura și temperatura - Temperatura - - Definiții - - - Pe baza principiului zero - - - Pe baza celui de al doilea principiu - - (...) Unități de temperatură - - Măsurarea temperaturii - - Temperatura în gaze - Căldura - - Istorie - - Transferuri de energie sub formă de căldură între două corpuri - - Notație și unități - Măsurarea căldurii - - Istorie - - Tehnologii - - - Termometria non-invazivă - - Temperatura aerului de suprafață - Capacitatea calorică - - Măsurare - - Capacitate calorică specifică - Dilatarea termică - - Prezentare generală - - - Prezicerea dilatării - - - Efecte de contracție (dilatare termică negativă) - - - Factorii care afectează dilatarea termică - - Coeficientul de dilatare termică - - - Coeficientul general de dilatare termică volumetrică - - Dilatarea în solide - - Dilatarea izobară în gaze - - Dilatarea în lichide Transferul de căldură - Conducția termică - - Prezentare generală - Convecția - - Exemple și aplicații ale convecției - - - Transfer de căldură - - - Circulația atmosferică - - - Vremea - - - Circulația oceanică - - - Convecția mantalei - - Mecanisme de convecție - - Convecția naturală - - - Convecția forțată - - - Convecția gravitațională sau flotabilitate - - - Convecția granulată - - - Convecția termomagnetică - - - Acțiunea capilară - - - Efectul Marangoni - - - Efectul Weissenberg - - - Combustia - Radiația termică - - Prezentare generală - - - Efecte de suprafață - - Proprietăți - Emisia de energie radiantă - - Emisivități ale suprafețelor obișnuite - - Emitanța - Absorbția energiei radiante - - Legea lui Kirchhoff a radiațiilor termice - - - Emisivitatea spectrală direcțională - - Cuantificarea absorbției - - Măsurarea absorbției - - Aplicații - Reflexia energiei radiante - - Reflectivitatea - - Tipul suprafeței - - Reflectanța apei - Răcirea radiativă - - Răcirea radiativă terestră - - - Energia Pământului - - - Răcirea nocturnă de suprafață - - - Estimarea lui Kelvin a vârstei Pământului - - Astronomie - - Aplicații - - - Arhitectură - - - Gheața nocturnă - Legea de răcire a lui Newton - - Relația cu mecanismul de răcire - - Versiunea de transfer termic a legii - Energia solară - Celule solare - - Tehnologii principale - - - Celule fotovoltaice - - - - Sisteme fotovoltaice convenționale - - - Energie solară concentrată - - - Sisteme hibride - - Tehnologii emergente - - - Celule fotovoltaice concentrate - - - Celule fotovoltaice plutitoare - Transferul termic - - Prezentare generală - - Inginerie - - - Izolare, radianță și rezistență - - - Dispozitive - - - Schimbătoare de căldură Schimbări climatice - Terminologie - Cauze - - Mecanisme interne de forțare - - Variabilitatea ocean-atmosferă - - - Viaţa - - Mecanisme externe de forțare - - - Variații orbitale - - - Variații solare - - - Vulcanism - - - Plăci tectonice - - - Influențe umane - Evidențe fizice - - Măsurători de temperatură și proxi-uri - - Dovezi istorice și arheologice - - Gheţarii - - Pierderea de gheață din Marea Arctică - - Vegetația - - - Resurse genetice forestiere - - Analiza polenului - - Acoperire de nori și precipitații - - Dendroclimatologia - - Mostre de gheață - - Animale - - Schimbarea nivelului mărilor - Efectul de seră - - Istorie - - Mecanism - - Gaze cu efect de seră - - Rolul schimbărilor climatice - Încălzirea globală - Note - Efecte observate și așteptate asupra mediului - - Vremea extremă - - Nivelul mării creste - - Sisteme ecologice - - Efecte pe termen lung - Efectele asupra sistemelor sociale - - Habitatul inundațiilor - - Economie - - Infrastructură Schimbarea de fază - Clasificarea tranzițiilor de fază - - Clasificarea Ehrenfest - - Clasificarea modernă a tranzițiilor de fază - Proprietăți ale tranzițiilor de fază - - Puncte critice - - Simetria - - Exponenți critici și clase de universalitate - Evaporarea - - Teorie - - - Echilibru evaporativ - - Factorii care influențează rata de evaporare - Condensarea - - Inițiere - - Scenarii de reversibilitate - - Cele mai frecvente scenarii - - Cum este măsurată condensarea - - Aplicații ale condensării - - Adaptarea biologică - - Condensarea în construcția de clădiri - Ceaţa - - Definiție - - Formare - Norii - - Formarea și distribuția - - - Cum devine saturat aerul - - - Convergența de-a lungul zonelor cu presiune scăzută - - - Divergența de-a lungul zonelor de înaltă presiune - - Efecte asupra climei și atmosferei - Fierberea - - Tipuri - - - Nucleația - - - Fluxul de căldură critic - - - Tranziția - - - Filmul - - - Distilarea - - Fierberea vs. evaporarea - Înghețarea/Solidificarea - - Cristalizare - - Suprarăcire - - Exotermicități - - Vitrificare - - Expansiune - - Înghețarea organismelor vii - - - Bacterii - - - Plante - - - Animale - - Conservarea alimentelor - Topirea - - Topirea ca o tranziție de fază de prim ordin - - Criteriile de topire - - Suprarăcirea - - Topirea solidelor amorfe (sticle) - Căldura latentă - - Folosire - - - Meteorologie - - Căldură latentă specifică Termodinamica - Introducere - Istorie - Legile termodinamicii - Concepte în termodinamică - - Substanţe care se pot descrie doar prin temperatură - - Substanţe care se pot descrie doar prin temperatură şi presiune - - Substanţe care se pot descrie prin temperatură, presiune şi potenţial chimic - - Substanţe care se pot descrie prin temperatură şi câmp magnetic - - Sisteme termodinamice - - Stări termodinamice - Zero absolut - Termodinamica aproape de zero absolut - - Relația cu condensatul Bose-Einstein - - Scări de temperatură absolută - Temperaturi negative - Energia internă - - Introducere - - - Funcțiile cardinale - - Descriere și definiție - - - Schimbări ale energiei interne - Prima lege a termodinamicii - - Declarația revizuită conceptual, conform abordării mecanice - - Descriere - Procese adiabatice - - Descriere - - Diferite aplicații ale ipotezei adiabatice - - Încălzirea și răcirea adiabatică - Meteorologia (Fizica norilor) - - Răcirea aerului până la punctul de rouă - - - Răcirea adiabatică: pachete în creștere de aer umed - - - - Ascendența frontală și ciclonică - - - - Ascendența convectivă - - - - Ascendența orografică - - - Răcirea non-adiabatică - - Adăugarea de umezeală în aer - - Suprasaturația - - Suprarăcirea - - Coliziune - coalescență - - Procesul Bergeron - - Coeziune și dizolvare - A doua lege a termodinamicii - - Introducere - - Principiul lui Carnot - - Formularea lui Clausius - - Formularea Kelvin - - Echivalența formulărilor Clausius și Kelvin - - Relația dintre formularea lui Kelvin și formularea lui Planck - - Formularea lui Planck - - Principiul Carathéodory - - Principiul lui Planck - - Formularea pentru un sistem care are o expresie cunoscută a energiei sale interne în funcție de variabilele sale de stare extinse - Motoare termice - - Prezentare generală - - Exemple de zi cu zi - - Exemple de motoare termice - - - Motorul termic al Pământului - - Eficienţa - - - Puterea - Ordinea și dezordinea - - Prezentare generală - Entropia - - Definiții - - - Definiţia statistică a entropiei: Principiul lui Boltzmann - - Funcția de stare - - Proces reversibil - - Entropia unui sistem - - Informaţiile fizice şi entropia Referințe Despre autor - Nicolae Sfetcu - - De același autor - - Contact Editura - MultiMedia Publishing . 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One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way that they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a probabilistic (...) one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his concept of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concepts that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover. (shrink)

In this paper we apply the popular Best System Account of laws to typical eternal worlds – both classical eternal worlds and eternal worlds of the kind posited by popular contemporary cosmological theories. We show that, according to the Best System Account, such worlds will have no laws that meaningfully constrain boundary conditions. It’s generally thought that lawful constraints on boundary conditions are required to avoid skeptical arguments. Thus the lack of such laws given the Best System Account may seem (...) like a severe problem for the view. We show, however, that at eternal worlds, lawful constraints on boundary conditions do little to help fend off skeptical worries. So with respect to handling these skeptical worries, the proponent of the Best System Account is no worse off than their competitors. (shrink)

In this article, it is argued that, for a classical Hamiltonian system which is closed, the ergodic theorem emerge from the Gibbs-Liouville theorem in the limit that the system has evolved for an infinitely long period of time. In this limit, from the perspective of an ignorant observer, who do not have perfect knowledge about the complete set of degrees of freedom for the system, distinctions between the possible states of the system, i.e. the information content, is lost leading to (...) the notion of statistical equilibrium where states are assigned equal probabilities. Finally, by linking the concept of entropy, which gives a measure for the amount of uncertainty, with the concept of information, the second law of thermodynamics is expressed in terms of the tendency of an observer to loose information over time. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

Why is our knowledge of the past so much more ‘expansive’ (to pick a suitably vague term) than our knowledge of the future, and what is the best way to capture the difference(s) (i.e., in what sense is knowledge of the past more ‘expansive’)? One could reasonably approach these questions by giving necessary conditions for different kinds of knowledge, and showing how some were satisfied by certain propositions about the past, and not by corresponding propositions about the future. I take (...) it that such is the approach of Chapter 6 of Time and Chance (T&C). Here’s another such a proposal, similar to that of, but significantly different from T&C; my purpose in this section is to highlight the differences, by showing how this account fails. (shrink)

A complete and up-to-date analysis of the question of time directionality as it arises in a semi-classical context is provided which is based on key developments related to the theory of gravitation. Important clarifications are achieved regarding the concept of time reversal as a concept independent from the thermodynamic arrow of time. The role played by the Leibnizian constraint of relational definition of physical properties applied to the sign of electric charge and the energy of elementary particles is thoroughly examined (...) and significant consequences of applying this consistency requirement are derived. This allows a better understanding of the general relativistic concept of stress-energy as a particular manifestation of zero-point vacuum fluctuations to emerge. A set of axioms are proposed which allow an integration of those concepts to the classical theory of gravitation. Those results are then applied to provide original solutions to several long-standing problems in theoretical cosmology, including the problem of the origin of thermodynamic time asymmetry and several other issues traditionally approached using inflation theory. (shrink)

In a world awash in statistical patterns, should we conclude that the universe’s evolution or genesis is somehow subject to chance? I draw attention to alternatives that must be acknowledged if we are to have an adequate assessment of what chance the universe might have had.

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests (...) interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics. (shrink)

Over the last two centuries, the relationship between philosophy and science has completely broken down, so the question we are confronted with is: How can we develop a new philosophy, which will influence science decisively? The physicists of the last century rejected their contemporary philosophy. They considered that “philosophy today is dead” (Hawking and Mlodinow 2010). However, we believe that the great scientific problems are always philosophical, and only philosophical problems. Therefore, these problems can be solved only by philosophers and (...) scientists who operate at the greatest level of thinking: that of the “paradigm of thinking”. In fact, these great scientific problems can usually be solved by changing the “paradigm of thinking” for scientists. This book furnished more applications of the “epistemologically different worlds” (that replaced the “world”/”universe” – in their previous books (2008, 2010, 2011, etc.), the authors indicated that the notion of the world/universe is wrong). Following Aristotle’s “Prime Mover” (or the “Unmoved Mover”), we stop the regress ad infinitum by discovering the first EW, the EW0 (the Hypernothing). Even if one EW does not exist for any EDW, the Hypernothing was the first EW and all other EDWs correspond to the EW0. Chapter 2 is about the “Hypernothing”. The other chapters continue our works of applying the EDWs to different concepts/areas of Physics: quantum mechanics, elementary particles, thermodynamics (with its main notion, “entropy”), etc. In the last chapter, knowing that Einstein’s special and general theory of relativity are very correct (but in a book 2016 we showed that “spacetime” cannot ontologically exist), we re-write both theories without “spacetime”. Content, Introduction and Chapter 1, FREE at https://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Daps&field-keywords=gabriel+vacariu&rh=i %3Aaps%2Ck%3Agabriel+vacariu . (shrink)

I present a new thermodynamic argument for the existence of God. Naturalistic physics provides evidence for the failure of induction, because it provides evidence that the past is not at all what you think it is, and your existence is just a momentary fluctuation. The fact that you are not a momentary fluctuation thus provides evidence for the existence of God – God would ensure that the past is roughly what we think it is, and you have been in existence (...) for roughly the amount of time you think you have. I don’t have a definitive way for the atheist to refute this argument, but I give one suggestion that relies on physics-based simplicity considerations. I close with an epistemological discussion of self-undermining arguments. (shrink)

Consider a gas confined to the left half of a container. Then remove the wall separating the two parts. The gas will start spreading and soon be evenly distributed over the entire available space. The gas has approached equilibrium. Why does the gas behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the system has to be ergodic for the approach to equilibrium to take place. This answer has been criticised on different grounds (...) and is now widely regarded as flawed. In this paper we argue that these criticisms have dismissed Boltzmann’s answer too quickly and that something almost like Boltzmann’s answer is true: the approach to equilibrium takes place if the system is epsilon-ergodic, i.e. ergodic on the entire accessible phase space except for a small region of measure epsilon. We introduce epsilon-ergodicity and argue that relevant systems in statistical mechanics are indeed espsilon-ergodic. (shrink)

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides general (...) criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions. (shrink)

This paper, written in Romanian, explains why the eutaxiological argument - endorsed by scientists like Newton, Einstein, and Weyl - is not a sound one.

Plausible assumptions from Cosmology and Statistical Mechanics entail that it is overwhelmingly likely that there will be exact duplicates of us in the distant future long after our deaths. Call such persons “Boltzmann duplicates,” after the great pioneer of Statistical Mechanics. In this paper, I argue that if survival of death is possible at all, then we almost surely will survive our deaths because there almost surely will be Boltzmann duplicates of us in the distant future that stand in appropriate (...) relations to us to guarantee our survival. (shrink)

The recent use of typicality in statistical mechanics for foundational purposes has stirred an important debate involving both philosophers and physicists. While this debate customarily focuses on technical issues, in this paper I try to approach the problem from an epistemological angle. The discussion is driven by two questions: (1) What does typicality add to the concept of measure? (2) What kind of explanation, if any, does typicality yield? By distinguishing the notions of `typicality-as-vast-majority' and `typicality-as-best-exemplar', I argue that the (...) former goes beyond the concept of measure. Furthermore, I also argue that typicality aims at providing us with a form of causal explanation of equilibrium. (shrink)

Metaphors establish connection. Root metaphors--patterns of relational imagery in the language and thought of a culture, in which a diverse group of tenors are related to a single indentifiable class of vehicles--play an important role in organizing our thought, and in bringing a coherence to our vision of the world. This is a political function; root metaphors, as philosopher Stephen Pepper discusses them, are most often found in the works of philosophers remembered as political philosophers. ;The second law of thermodynamics--the (...) law of entropy--holds that in any spontaneous process, usable energy becomes unusable energy. It also suggests that improbable order must succumb, through time, to more probable chaos. The law of entropy has enjoyed a popularity as metaphor unusual for such physics esoterica. In the works of Brooks Adams, Henry Adams, Nicholas Georgescu-Roegen, and Thomas Pynchon, the idea of entropy appears as the fundamental, organizing idea for an economic interpretation of history, a philosophy of history, an ecologically enlightened economic theory, and an encyclopedic novel that apotheosizes modern culture. Analysis of how the entropy metaphor is manifest in the works of these thinkers allows us to judge the strengths and weaknesses of entropy as root metaphor. Analysis of its contemporary popularity affords insight into the politics of the day. Ultimately, the entropy root metaphor serves as the foundation of a refurbished "generating substance" world hypothesis, but the root metaphor itself remains equivocal on the important issue of centralized versus decentralized political organization. (shrink)

Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to the largest (...) macro-region. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. (shrink)

We refer to the remarkable thought of Erwin Schrödinger expressed in his book “What is life?” regarding the connection between life and a decrease of entropy realized via feeding (eating). This thought is “transferred” into the field of human psychology, explaining hooligan behavior (e.g. the “days of violence”) as a natural human response to the improper (in its content or form) “informational feeding” that does not allow one to normally treat (‘’digest”) the received information, i.e. to make ones thoughts simpler (...) in their logical structure. Delivering information without pedagogical, psychological, and (when children are involved) neurological supervision or assistance is supposed to be the cause for the hooliganism that more and more often obtains a dangerous organized form. (shrink)

This doctoral dissertation investigates the notion of physical necessity. Specifically, it studies whether it is possible to account for non-accidental regularities without the standard assumption of a pre-existent set of governing laws. Thus, it takes side with the so called deflationist accounts of laws of nature, like the humean or the antirealist. The specific aim is to complement such accounts by providing a missing explanation of the appearance of physical necessity. In order to provide an explanation, I recur to fields (...) that have not been appealed to so far in discussions about the metaphysics of laws. Namely, I recur to complex systems’ theory, and to the foundations of statistical mechanics. The explanation proposed is inspired by how complex systems’ theory has elucidated the way patterns emerge, and by the probabilistic explanations of the 2nd law of thermodynamics. More specifically, this thesis studies how some constraints that make no direct reference to the dynamics can be a sufficient condition for obtaining in the long run, with high probability, stable regular behavior. I hope to show how certain metaphysical accounts of laws might benefit from the insights achieved in these other fields. According to the proposal studied in this thesis, some regularities are not accidental not in virtue of an underlying physical necessity. The non-accidental character of certain regular behavior is only due to its overwhelming stability. Thus, from this point of view the goal becomes to explain the stability of temporal patterns without assuming a set of pre-existent guiding laws. It is argued that the stability can be the result of a process of convergence to simpler and stable regularities from a more complex lower level. According to this project, if successful, there would be no need to postulate a (mysterious) intermediate category between logical necessity and pure contingency. Similarly, there would be no need to postulate a (mysterious) set of pre-existent governing laws. Part I of the thesis motivates part II, mostly by arguing why further explanation of the notions of physical necessity and governing laws should be welcomed (chapter 1), and by studying the plausibility of a lawless fundamental level (chapters 2 and 3). Given so, part II develops the explanation of formation of simpler and stable behavior from a more complex underlying level. (shrink)

A differenza della meccanica quantistica, i cui fondamenti sono sempre stati al centro di un ininterrotto dibattito, gli aspetti concettuali della meccanica statistica non hanno attratto interessi così vasti; tra le eccezioni citiamo il bel libro di Emch e Liu. In questo breve contributo discuteremo alcuni problemi concettuali della meccanica statistica, in particolare il ruolo del caos e l’emergenza di proprietà collettive che appaiono quando il numero delle particelle del sistema è molto grande.

One popular approach to statistical mechanics understands statistical mechanical probabilities as measures of rational indifference. Naive formulations of this ``indifference approach'' face reversibility worries - while they yield the right prescriptions regarding future events, they yield the wrong prescriptions regarding past events. This paper begins by showing how the indifference approach can overcome the standard reversibility worries by appealing to the Past Hypothesis. But, the paper argues, positing a Past Hypothesis doesn't free the indifference approach from all reversibility worries. For (...) while appealing to the Past Hypothesis allows it to escape one kind of reversibility worry, it makes it susceptible to another - the Meta-Reversibility Objection. And there is no easy way for the indifference approach to escape the Meta-Reversibility Objection. As a result, reversibility worries pose a steep challenge to the viability of the indifference approach. (shrink)

International Studies in the Philosophy of Science, Volume 27, Issue 3, Page 273-293, September 2013.

Why does classical equilibrium statistical mechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcanonical exist. In response I define the generalized properties of epsilon-ergodicity and epsilon-continuity, I review computational evidence indicating that systems of interest are epsilon-ergodic, I adapt Malament and Zabell’s (...) defense of absolute continuity to support epsilon-continuity, and I prove that, for epsilon-ergodic systems, every epsilon-continuous invariant probability measure is very close to the microcanonical. (shrink)

I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...) proposing a third modification of Lewis's theory, one which explains many of the common features shared by the chance theories of physics. (shrink)

I assess the thesis that counterfactual asymmetries are explained by an asymmetry of the global entropy at the temporal boundaries of the universe, by developing a method of evaluating counterfactuals that includes, as a background assumption, the low entropy of the early universe. The resulting theory attempts to vindicate the common practice of holding the past mostly fixed under counterfactual supposition while at the same time allowing the counterfactual's antecedent to obtain by a natural physical development. Although the theory has (...) some success in evaluating a wide variety of ordinary counterfactuals, it fails as an explanation of counterfactual asymmetry. (shrink)

I defend what may loosely be called an eliminativist account of causation by showing how several of the main features of causation, namely asymmetry, transitivity, and necessitation, arise from the combination of fundamental dynamical laws and a special constraint on the macroscopic structure of matter in the past. At the microscopic level, the causal features of necessitation and transitivity are grounded, but not the asymmetry. At the coarse-grained level of the macroscopic physics, the causal asymmetry is grounded, but not the (...) necessitation or transitivity. Thus, at no single level of description does the physics justify the conditions that are taken to be constitutive of causation. Nevertheless, if we mix our reasoning about the microscopic and macroscopic descriptions, the structure provided by the dynamics and special initial conditions can justify the folk concept of causation to a significant extent. I explain why our causal concept works so well even though at bottom it is comprised of a patchwork of principles that don't mesh well. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The second of these articles discusses the regularity approach to statistical mechanical probabilities, and describes some areas (...) where further research is needed. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...) to statistical mechanical probabilities. (shrink)

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of (...) time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

The Kolmogorov-Sinai entropy is a fairly exotic mathematical concept which has recently aroused some interest on the philosophers’ part. The most salient trait of this concept is its working as a junction between such diverse ambits as statistical mechanics, information theory and algorithm theory. In this paper I argue that, in order to understand this very special feature of the Kolmogorov-Sinai entropy, is essential to reconstruct its genealogy. Somewhat surprisingly, this story takes us as far back as the beginning of (...) celestial mechanics and through some of the most exciting developments of mathematical physics of the 19th century. (shrink)

I conduct an empirical analysis of the temporally asymmetric character of our epistemic access to the world by providing an experimental scheme whose results represent the core empirical content of the epistemic asymmetry. I augment this empirical content by formulating a gedanken experiment inspired by a proposal from David Albert. This second experiment cannot be conducted using any technology that is likely to be developed in the foreseeable future, but the expected results help us to state an important constraint on (...) our ability to know the future. Finally, I show that a third experiment concerning precognition, described by Michael Scriven and John Mackie, does not characterize any additional empirical content but does help to illustrate why it is unlikely that any precognition exists. (shrink)

I provide a comprehensive metaphysics of causation based on the idea that fundamentally things are governed by the laws of physics, and that derivatively difference-making can be assessed in terms of what fundamental laws of physics imply for hypothesized events. Highlights include a general philosophical methodology, the fundamental/derivative distinction, and my mature account of causal asymmetry.

An explanation of our seeming inability to influence the past.

The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics (...) system. As a result, there is no entropic force in the gravity system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This provides a further support for the conclusion that gravity is not an entropic force. (shrink)