The Second Law

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01 September 2017

09:30 - 10:00 Coffee and Snacks, Registration

10:00 - 11:15 Aron Wall: The Generalized Second Law and Singularity Theorems
11:15 - 11:30 Coffee Break
11:30 - 12:30 Carina Prunkl and Katherine Robertson: Thermodynamics Without Observers?
12:30 - 13:45 Lunch

13:45 - 15:00 Alison Fernandes: The Temporal Asymmetry of Chance
15:00 - 15:15 Coffee Break
15:15 - 16:15 Marc Holman: Quantum Gravity, Temporal Asymmetry and the Second Law of Thermodynamics
16:15 - 16:45 Coffee and Snacks

16:45 - 18:00 David Wallace: Probability and Irreversibility in Modern Statistical Mechanics: Classical and Quantum
19:00 Conference Dinner

02 September 2017

09:30 - 10:00 Coffee and Snacks
10:00 - 11:15 Giovanni Valente: Time and Irreversibility in Axiomatic Thermodynamics
11:15 - 11:30 Coffee Break
11:30 - 12:30 Patricia Palacios: Had We But World Enough, and Time, But We Don’t!: Justifying the Thermodynamic and Infinite-time Limits in Statistical Mechanics
12:30 - 13:45 Lunch
13:45 - 15:00 Charlotte Werndl: Boltzmann versus Gibbs: Phase Transitions
15:00 - 15:15 Coffee Break
15:15 - 16:15 Dustin Lazarovici: Thermodynamic Arrow Without Past Hypothesis
16:15 - 16:45 Coffee and Snacks

16:45 - 18:00 TBA


The Temporal Asymmetry of Chance

Alison Fernandes (University of Warwick)

We derive the Second Law of thermodynamics from the fact that isolated systems at non-maximal entropy have an overwhelmingly high chance of increasing in entropy over time. Such derivations seem to make ineliminable use of objective chances. But some have argued that if the fundamental laws are deterministic, there can be no genuine objective chances (Popper, Lewis, Schaffer). Statistical-mechanical chances are merely epistemic, or otherwise less real than dynamical chances. Many have also thought that chance is fundamentally temporally asymmetric. It is part of the nature of chance that the past is ‘fixed’, and that only future events have non-trivial chances. I’ll argue that it is no coincidence that many have held both views: the rejection of deterministic chance is driven by an asymmetric picture of chance in which the past produces the future. I’ll articulate a more deflationary view, according to which more limited temporal asymmetries in chance reflect contingent asymmetries of precisely the kind embodied in the Second Law. The past can be chancy. Does this view entail a kind of ‘best-systems’ account according to which chances merely summarise information about events? I’ll end with some brief thoughts on why such a view is troubling, and suggest an

Quantum Gravity, Temporal Asymmetry and the Second Law of Thermodynamics

Marc Holman (University of Western Ontario)

A fundamental problem with attempts to explain the Second Law of Thermodynamics in terms of a cosmological boundary condition is that there is at present no well defined measure of gravitational entropy. After reviewing this situation in some depth, while also taking note of some well-known caveats that this type of approach runs into in general, I will argue that a future theory of ''quantum gravity'' is exactly what is needed to properly address these

Thermodynamic Arrow Without Past Hypothesis

Dustin Lazarovici (University of Lausanne)

Today, the great puzzle about the second law of thermodynamics is not why entropy will typically increase from a non-equilibrium value but why we find systems -- and ultimately our universe -- in a non-equilibrium state to begin with. More precisely, the explanation of the thermodynamic arrow seems to require a "Past Hypothesis", the assumption of an atypical (low-entropy) initial macrostate of the universe.

We will discuss a more recent proposal by Sean Carroll and Jennifer Chen who suggest that the universe has no equilibrium state, so that entropy can increase without bound. This model is intriguing because it seeks to establish the existence of a thermodynamic arrow as features of a typical universe, without the need to postulate a special initial state. We will point out that a classical gravitating system provides a possible model for such a universe, drawing parallels to recent works of Julian Barbour and collaborators, who make related observations in the framework of their shape dynamics. We will then discuss if the Carroll model can really succeed in grounding sensible statistical inferences about the thermodynamic history of our universe without assuming (something akin to) a Past

Had We But World Enough, and Time, But We Don’t!: Justifying the Thermodynamic and Infinite-time Limits in Statistical Mechanics

Patricia Palacios (LMU Munich/MCMP)

In this contribution, I compare the use of the thermodynamic limit in the theory of phase transitions with the infinite-time limit in the explanation of equilibrium statistical mechanics. In the case of phase transitions, I will argue that the thermodynamic limit can be justified pragmatically since the limit behavior (i) also arises before we get to the limit and (ii) for values of N that are physically significant. However, I will contend that the justification of the infinite-time limit is less straightforward. In fact, I will point out that even in cases where one can recover the limit behavior for finite t, i.e. before we get to the limit, one cannot recover this behavior for realistic time scales. I will claim that this leads us to reconsider the role that the rate of convergence plays in the justification of infinite limits and calls for a revision of the so-called Butterfield’s

Thermodynamics without Observers?

Carina Prunkl (University of Oxford) and Katherine Robertson (University of Cambridge)

Boltzmannians often criticise the Jaynesian approach to statistical mechanics for being too subjective or anthropocentric, and thus unfaithful to the phenomenological theory of thermodynamics it putatively reduces. Yet, should we think thermodynamics is an objective theory? In this paper, we consider two reasons why thermodynamics may be considered anthropocentric: the work/heat distinction and the role of agents intervening on systems. However, by considering quantum thermodynamics, and the role of different levels of description in science more generally, we conclude that thermodynamics is not worrying anthropocentric - at least, not in a way different from other scientific

Time and Irreversibility in Axiomatic Thermodynamics

Giovanni Valente (University of Pittsburgh)

This talk is based on join work with Robert Marsland III and Harvey Brown and deals with the issues of time and irreversibility as they arise in axiomatic thermodynamics. Thermodynamics is the paradigm example in physics of a time-asymmetric theory, but the origin of the asymmetry lies deeper than the second law. A primordial arrow can be defined by the way of the equilibration principle (“minus first law”). By appealing to this arrow, the nature of the well-known ambiguity in Carathéodory’s 1909 version of the second law becomes clear. Following Carathéodory’s seminal work, formulations of thermodynamics have gained ground that highlight the role of the binary relation of adiabatic accessibility between equilibrium states, the most prominent recent example being the important 1999 axiomatization due to Lieb and Yngvason. This formulation can be shown to contain an ambiguity strictly analogous to that in Carathéodory’s

The Generalized Second Law and its Implications for Spacetime Geometry

Aron Wall (Stanford University)

The generalized second law (GSL) states that the area of black hole horizons, plus any matter entropy outside of them, cannot decrease as time passes. I will review the current status of this seeming law of nature, including the controversial question of which definition of "horizon" should be used. There now exist semiclassical proofs of the GSL when the horizon is coupled to arbitrary quantum field theories. While its ultimate explanation in terms of quantum gravity statistical mechanics is still unknown, it seems to be related to the "holographic principle", the idea that the information in a region of space can (at least sometimes) be encoded in the data in the boundary of that region.

In the second half of the talk, I will argue that the GSL can be used to generalize the Penrose singularity theorem to quantum gravitational situations. This suggests that spacetime singularities, in the sense of an edge of spacetime, will not be resolved by quantum gravity effects. This can also be used to rule out various kinds of causality violating spacetimes: e.g. traversable wormholes, warp drives, and time

Probability and Irreversibility in Modern Statistical Mechanics: Classical and Quantum

David Wallace (University of Southern California)

Through consideration of two wide classes of case studies --- dilute gases and linear systems --- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the latter is understood as primarily concerned with the derivation of quantitative higher-level equations of motion, and only derivatively with underpinning the equilibrium concept in thermodynamics. I argue that at least in this wide class of examples, (i) irreversibility is introduced through a reasonably well-defined initial-state condition which does not precisely map onto those in the extant philosophical literature; (ii) probability is explicitly required both in the foundations and in the predictions of the theory. I then consider the same examples, as well as the more general context, in the light of quantum mechanics, and demonstrate that while the analysis of irreversiblity is largely unaffected by quantum considerations, the notion of statistical-mechanical probability is entirely reduced to quantum-mechanical

Boltzmann versus Gibbs: Phase Transitions

Charlotte Werndl (University of Salzburg)

Abstract: There are two main theoretical frameworks in statistical mechanics, one associated with Boltzmann and the other with Gibbs. Despite their well-known differences, there is a prevailing view that equilibrium values calculated in both frameworks coincide. We show that this is wrong by giving examples of phase transitions where the two frameworks diverge. In these cases the Boltzmannian treatment delivers the correct empirical results but the Gibbsian framework does not. Based on these examples, we argue that Boltzmannian statistical mechanics is the fundamental theory and Gibbsian statistical mechanics is best interpreted as an effective theory.