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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 longrun 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 (...) 

Gibbsian statistical mechanics is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental practice. The root cause of the difficulties is the status of the Averaging Principle, the proposition that what we observe in an experiment is the ensemble average of a phase function. We review different stances toward this principle, and eventually present a coherent interpretation (...) 

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics. 

I highlight that the aim of using statistical mechanics to underpin irreversible processes is, strictly speaking, ambiguous. Traditionally, however, the task of underpinning irreversible processes has been thought to be synonymous with underpinning the Second Law of thermodynamics. I claim that contributors to the foundational discussion are best interpreted as aiming to provide a microphysical justification of the Minus First Law, despite the ways their aims are often stated. I suggest that contributors should aim at accounting for both the Minus (...) 

In Boltzmannian statistical mechanics macrostates supervene on microstates. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable microstates. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality (...) 

We discuss Boltzmann’s probabilistic explanation of the second law of thermodynamics providing a comprehensive presentation of what is called today the typicality account. Countering its misconception as an alternative explanation, we examine the relation between Boltzmann’s Htheorem and the general typicality argument demonstrating the conceptual continuity between the two. We then discuss the philosophical dimensions of the concept of typicality and its relevance for scientific reasoning in general, in particular for understanding the reduction of macroscopic laws to microscopic laws. Finally, (...) 

I provide a selfcontained introduction to the problem of the arrow of time in physics, concentrating on the irreversibility of dynamical processes as described in statistical mechanics. 

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measuretheoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main (...) 

Boltzmannian statistical mechanics partitions the phase space of a sys tem into macroregions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the MaxwellBoltzmann 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 (...) 

A gas prepared in a nonequilibrium state will approach equilibrium and stay there. An influential contemporary approach to Statistical Mechanics explains this behaviour in terms of typicality. However, this explanation has been criticised as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases which are epsilonergodic are typical with respect to the Whitney topology. Because equilibrium states are typical, (...) 

This thesis makes the issue of reconciling the existence of thermodynamically irreversible processes with underlying reversible dynamics clear, so as to help explain what philosophers mean when they say that an aim of nonequilibrium statistical mechanics is to underpin aspects of thermodynamics. Many of the leading attempts to reconcile the existence of thermodynamically irreversible processes with underlying reversible dynamics proceed by way of discussions that attempt to underpin the following qualitative facts: that isolated macroscopic systems that begin away from equilibrium (...) 

Kevin Davey claims that the justification of the second law of thermodynamics as it is conveyed by the “standard story” of statistical mechanics, roughly speaking, that lowentropy microstates tend to evolve to highentropy microstates, is “unhelpful at best and wrong at worst.” In reply, I demonstrate that Davey’s argument for rejecting the standard story commits him to a form of skepticism that is more radical than the position he claims to be stating and that Davey places unreasonable demands on the (...) 