The Second Law
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Program

01 September 2017

TimeEvent
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 Katie 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 Dustin Lazarovici: Thermodynamic Arrow Without Past Hypothesis
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

TimeEvent
09:30 - 10:00 Coffee and Snacks
10:00 - 11:15 Giovanni Valente: On the Paradox of Reversible Processes in 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
 Break
13:45 - 15:00 Charlotte Werndl: Boltzmann versus Gibbs: Phase Transitions
15:00 - 15:15 Coffee Break
15:15 - 16:15 Mathias Frisch: The Second Law and the Arrow of Radiation: Re-assessing the Ritz-Einstein Debate

Abstracts

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 are overwhelmingly likely to increase in entropy over time. Such derivations seem to make ineliminable use of objective worldly probabilities (chances). But some have argued that if the fundamental laws are deterministic, there can be no non-trivial chances (Popper, Lewis, Schaffer). Statistical-mechanical probabilities are merely epistemic, or otherwise less real than ‘dynamical’ chances. Many have also thought that chance is intrinsically temporally asymmetric. It is part of the nature of chance that the past is ‘fixed’, and that non-trivial chances are only of future events. I’ll argue that it is no coincidence that many have held both views: the rejection of deterministic chance is tied to 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 reflected in the Second Law. The past can be chancy.
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Mathias Frisch: The Second Law and the Arrow of Radiation: Re-assessing the Ritz-Einstein Debate

In 1909 Ritz and Einstein debated the nature of the arrow of radiation in a series of papers in the Physikalische Zeitschrift. Their debate culminated in a joint letter in which they agreed to disagree. Einstein, the letter claims, took the radiation asymmetry to be thermodynamic origin, while Ritz took it to be fundamental. Contemporary commentators tend to side with Einstein. In this talk I want to re-examine the Ritz-Einstein and argue that Einstein's views do not lend unequivocal support to the reductivist position.

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 difficulties.top

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 Hypothesis.top

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 principle.top

Thermodynamics without Observers?

Carina Prunkl (University of Oxford) and Katie 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 theories.top

On the Paradox of Reversible Processes in Thermodynamics

Giovanni Valente (University of Pittsburgh)

This paper discusses an argument by Norton (2014, 2016) to the effect that reversible processes in thermodynamics have paradoxical character, due to the infinite-time limit. For Norton, one can "dispel the fog of paradox" by adopting a distinction between idealizations and approximations, which he himself puts forward. Accordingly, reversible processes ought to be regarded as approximations, rather than idealizations. Here, we critically assess his proposal. In doing so, we offer a resolution of his alleged paradox based on the original work by Tatiana Ehrenfest-Afanassjeva on the foundations of thermodynamics.
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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 machines.top

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 probability.top

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.