## Philosophy of Physics Workshop: Foundations of Thermodynamics 2024

### 16 June 2024 - 18 June 2024

### EVENT DESCRIPTION

In the past few decades there has been a transformation—some have called it a revolution—in the way that many physicists are approaching the science of thermodynamics. Philosophers of science have only recently begun to take notice of this transformation. This workshop, which brings together philosophers and physicists at is inspired by the conviction that this shift in thermodynamics has the potential to transform the long-standing philosophical and foundational discussions of thermodynamics and statistical mechanics, and that philosophers have a role to play in elucidating the significance of the new perspective on thermodynamics. The workshop is hybrid in format: half of the speakers will be participating in person, and the other half, remotely.

All are welcome! Please register, so that we can get an idea of numbers for catering purposes (for those who are attending in person), and to receive the Zoom link, if you’re attending remotely.

*This workshop is supported by the Rotman Institute of Philosophy, the Department of Philsophy, IQOQI, The Faculty of Arts & Humanities, Research Western. Additional funding is provided by a SSHRC Connection Grant.*

**Questions? Reach out! Contact us at thermoconference2024@uwo.ca**

**Philosophy of Thermodynamics Workshop Schedule DAY 1**

### Sunday, June 16

9:00 a.m. – 5:30 p.m.

Room TBD

9:00–10:30 **Markus Müller**, “Exact characterization of entropy and free energy without thermodynamic limit or averaging” (remote)

10:30–10:45 Coffee break

10:45–12:15 **Katie Robertson**, “How statistical mechanical probabilities emerge from entanglement” (remote).

12:15–14:00 Lunch

14:00–15:30 **Wayne Myrvold**, “Thermodynamics without entropy” (in-person)

15:30–16:00 Coffee break

16:00–17:30 **David Wallace**, “Thermodynamics with and without irreversibility” (in-person)

**Philosophy of Thermodynamics Workshop Schedule Day 2**

### Monday, June 17

9:00 a.m. – 5:30 p.m.

Room TBD

9:00–10:30 **Saakshi Dulani**, “Facing the Phantom Music: Black Hole Entropy Guides Information Conservation” (remote)

10:45–12:15 **Nicole Yunger Halpern**, “Beyond the First Law: Peculiarly quantum conservation laws in thermodynamics” (remote)

12:15–14:00 Lunch

14:00–15:30 **Billy Braasch**, “Non-Abelian transport distinguishes three usually equivalent notions of entropy production” (in-person)

15:30–16:00 Coffee break

16:00–17:30 **Eugene Chua**, “Pressure under pressure: on the status of the classical pressure in relativity” (in-person)

**Philosophy of Thermodynamics Workshop Schedule Day 3**

### Tuesday, June 18

9:30 a.m. – 12:45 p.m.

Room TBD

9:30–11:00 **Patricia Palacios**, “Re-defining equilibrium for long-range interacting systems**”**(remote)

11:00–11:15 Coffee break

**11:15****–12:45 Sean Carroll**, “Complexogenesis” (in-person)

**Billy Braasch**(in -person)

NRC Postdoctoral Fellow at the National Institute of Standards and Technology NIST and Joint Center for Quantum Information and Computer Science, University of Maryland

*Non-Abelian transport distinguishes three usually equivalent notions of entropy production*

A fundamental challenge is to define quantum thermodynamic quantities—for example, heat, work, and entropy production. We extend the definition of entropy production to a deeply quantum regime involving noncommuting observables. Consider two systems prepared in different thermal states. The systems can exchange some physical quantities (“charges”). There are three formulas that are commonly used to measure the entropy produced. These cast entropy as (1) an extensive thermodynamic variable, (2) an information-theoretic uncertainty measure, and (3) a quantifier of irreversibility. Typically, the charges are assumed to commute with each other (e.g., energy and particle number), meaning that they can be simultaneously measured. When this is true, the three entropy production formulas yield the same result. Yet quantum charges can fail to commute, inviting generalizations of the three formulae. Charges’ noncommutation, we find, breaks the formulae’s equivalence. Furthermore, different formulae quantify different physical effects of charges’ noncommutation on entropy production.

**
Sean Carroll **(in-person)

Homewood Professor of Natural Philosophy, Johns Hopkins University and Fractal Faculty, Santa Fe Institute

*Complexogenesis*

Increasing entropy is often glossed as increasing disorder or randomness. But in the evolution from the low-entropy early universe to the high-entropy future, complex structures apparently come into existence along the way. This isn’t in violation of the Second Law, as the formation and persistence of complex structures can be entropy-increasing processes; but it does raise the question of whether the appearance of complexity is automatic, and what kinds of rules govern it. I will propose a classification of different kinds of complex physical structures, discuss when and how they arise dynamically in undirected thermodynamic evolution, and relate them to issues of information and statistical physics.

**Eugene Chua** (in-person)

Ahmanson Postdoctoral Instructor in Philosophy of Science, California Institute of Technology

*Pressure under pressure: on the status of the classical pressure in relativity*

Much of the century-old debate surrounding the status of thermodynamics in relativity has centered on the search for a suitably relativistic temperature; recent work by Chua (2023) has suggested that ‘the’ classical temperature concept — consilient as it is in classical settings — ‘falls apart’ in relativity. However, these discussions have still tended to assume an unproblematic Lorentz transformation for ‘the’ pressure concept (specifically, this is presumed to be Lorentz invariant). Here I argue that, just like ‘the’ classical temperature, ‘the’ classical concept of pressure breaks down in relativistic settings. This situation suggests a new thermodynamic limit — a ‘rest frame’ limit — without which an unambiguous thermodynamic description of systems does not emerge. I end by briefly discussing how thermodynamics, in requiring preferred frames, bears on the idea of ‘symmetry-to-reality’ inferences.

**Saakshi Dulani **(remote)

Postdoctoral Fellow, Department of Philosophy, Johns Hopkins University

*Facing the Phantom Music: Black Hole Entropy Guides Information Conservation*

Planckian remnants. Baby universes. White holes. Catastrophic membranes. Soft hairs. Wormholes. Holograms. Fuzzballs. The list of prospective solutions to the black hole information loss paradox goes on and on. Despite innovations in the study of black hole evaporation and quantum gravity, we’re not much closer today than we were 30 years ago to narrowing down a solution.

To elucidate the root of the tension, I group the leading quantum gravity proposals into two, mutually exclusive categories: 1) safehouse solutions and 2) evacuation solutions. They’re differentiated by the following criterion. By the time an evaporating black hole reaches Planck mass, either: 1) Hawking radiation is maximally entangled with the interior, or 2) it’s barely entangled with the interior. I label proposals belonging to the first category ‘safehouse solutions’ because ostensibly missing information has been safely stored inside the black hole. I label proposals belonging to the second category ‘evacuation solutions’ because hidden information has instead been evacuated to the exterior.

These two categories map onto opposing conceptions of how black hole evaporation plays out, with sensitive implications for black hole thermodynamics and statistical mechanics. In response to this conundrum, I argue that we must rely on a hefty guiding principle to facilitate vetting proposals. I recommend my formulation of the Universality Argument (UA), which embraces multiply realized thermodynamic behaviors across self-gravitating and non-gravitating systems alike. It also prescribes common reduction methods into the statistical mechanics of microscopic constituents, for which the account of black hole entropy is crucial.

However, unlike terrestrial systems, black holes classically possess causal barriers known as event horizons, from which nothing traveling at or slower than the speed of light can escape. So, cashing out physically salient similarities between the two types of systems when applying UA is a nontrivial task. I claim that the disagreement in the discourse boils down to diverging intuitions about the strictness of the event horizon when quantum effects are added. This leads to competing statistical interpretations of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy, especially the question of whether its proportionality to horizon area motivates a universal entropy bound.

I further contend that both camps currently falter in underwriting thermodynamic phenomenology with the statistics of Bekenstein-Hawking degrees of freedom, though for different reasons. Two preliminary criteria that pit them against each other are black holes’ capabilities to mediate thermal contact and satisfy idealized conditions for thermal radiation. Therefore, the interpretation of Bekenstein-Hawking entropy and its role in reducing black hole thermodynamics to black hole statistical mechanics is a hypothesis to be tested against UA’s determination of relevant multiply realized phenomena. Further work needs to be done to make either camp more convincing vis-a-vis UA.

**Markus Müller** (remote)

Research Group Leader, Institute for Quantum Optics and Quantum Information (IQOQI) Vienna

*Exact characterization of entropy and free energy without thermodynamic limit or averaging*

We usually think of quantities like Helmholtz free energy F and von Neumann entropy S as attaining their physical meaning in the thermodynamic limit: for example, the second law is only true for large numbers of particles or on average. Similarly, information-theoretic quantities like von Neumann entropy only tell us operational facts (such as the achievable transmission rate) in the limit of infinitely long messages. Here, however, I describe a physical, operational interpretation of F and S that holds exactly, without fluctuations, and without averaging or thermodynamic limit, for single, small quantum systems. This interpretation follows from the resource-theoretic approach: the (im)possibility of state transitions in thermodynamics or information theory is exactly characterized by F or S if the (thermodynamic or catalytic) machine is allowed to become correlated or entangled with the work medium, while (as always) exactly preserving its own state. This feature becomes inessential in the thermodynamic limit, but it turns out to be crucial in the nanoscale. Furthermore, I present a no-go theorem (“no broadcasting of coherence and asymmetry”) showing that this theorem cannot hold in the presence of genuine quntum coherence between energy levels, and I give a brief outline on further implications for quantum information theory.

References:

M. P. Müller, Correlating Thermal Machines and the Second Law at the Nanoscale, Phys. Rev. X 8, 041051 (2018). DOI:10.1103/PhysRevX.8.041051.

M. Lostaglio and M. P. Müller, Coherence and Asymmetry Cannot be Broadcast, Phys. Rev. Lett. 123, 020402 (2019). DOI:10.1103/PhysRevLett.123.020403; arXiv:1812.08214.

P. Boes, J. Eisert, R. Gallego, M. P. Müller, and H. Wilming, Von Neumann Entropy from Unitarity, Phys. Rev. Lett. 122, 210402 (2019). DOI:10.1103/PhysRevLett.122.210402; arXiv:1807.08773.

**Wayne Myrvold** (in-person)

Department of Philosophy, The University of Western Ontario

*Thermodynamics without entropy*

On a resource-theoretic conception of thermodynamics, entropy, and other key thermodynamic concepts, are defined relative to a class of available manipulations. In particular, entropy is defined in terms of thermodynamically reversible processes connecting thermal states.

As has often been pointed out, most forcefully by Norton (2016), there are, strictly speaking, no thermodynamically reversible processes. Talk of reversible processes should be regarded as short-hand for talk of limiting properties of families of irreversible processes. Standard thermodynamics is recovered if reversibility can be approximated arbitrarily closely.

But what if we’re in a context in which arbitrarily good approximations to reversibility are lacking? Building on work in Myrvold (2020), I show how to formulate thermodynamics in the absence of a thermodynamic entropy function. Surprisingly, little is lost, as long as one is careful to respect distinctions (such as a distinction between dissipation and inefficiency) that collapse into each other when reversibility is assumed.

Norton, John D. (2016): ‘The Impossible Process: Thermodynamic Reversibility’, *Studies in **History and Philosophy of Modern Physics*, 55, pp. 43–61.

Myrvold, Wayne C. (2020): ‘The science of ΘΔ^{cs}’, *Foundations of Physics* **50** 1219–1251.

**Patricia Palacios** (remote)

*Re-defining equilibrium for long-range interacting systems*

Long-range interacting systems (LRI) are systems in which the interaction potential decays slowly for large inter-particle distance. Typical examples of long-range interactions are the gravitational and Coulomb forces. The philosophical interest for studying these kinds of systems has to do with the fact that they exhibit properties that escape traditional definitions of equilibrium based on stationary probability distributions. How should we define equilibrium for LRI, then? In this contribution, I argue that a comparison with ergodicity-breaking phase transitions gives us a qualitative understanding of equilibrium for these kinds of systems in terms of metastable equilibria. As in the case of phase transitions, I contend that in LRI one could account for metastable equilibria by defining the dynamics for finite-time scales. However, in contrast to phase transitions, I argue that these metastable states depend on unknown initial conditions and do not correspond to Boltzmannian equilibrium. This negative conclusion provides a possible basis for future scientific research.

**Katie Robertson** (remote)

*How statistical mechanical probabilities emerge from entanglement *

Probabilities in classical statistical mechanics are usually said to be introduced because we don’t know the exact microstate of the system. This has led to three sorts of concern: (i) concerns about the probabilities being subjective or tied to us, Albert (2000) (ii) concerns that there is a mismatch between the thermodynamic entropy defined in terms of the system’s individual state and the Gibbs entropy defined in terms of SM probabilities Callender (2001) and (iii) concerns that adding these probabilities in is helping ourselves to too much when thinking about reduction Sklar (1993). But the quantum case is radically different; it has its own source of probabilities (cf. Wallace (2015)). In this talk, I show how these quantum probabilities lead to the right statistical mechanical probabilities — the familiar microcanonical and canonical distributions, by relying on results from Popescu et al. (2005). The core insight is that most statistical mechanical systems are interacting with an environment (such as a heat bath) and thus are entangled. When we describe the system on its own (by tracing out the bath) we end up with an intrinsically probabilistic state. But showing that this state has the right form (i.e. approximates the canonically distributed state), and under what conditions it does so is complex, and discussed by Popescu et al. (2005). In particular, there are interesting questions about how the cases for which the Popescu result does not hold are related to the cases, or initial states, for which the method of arbitrary functions results do not hold. But there is one natural connection: the statistical mechanical probabilities have quantum probabilities as their source, but are nonetheless archetypal examples of ‘higher-level’ probabilities.

This project gives a new perspective of the nature of SM probabilities — as emerging from entanglement – and allows us to solve the above problems. I then tackle a challenge to this view from Myrvold (2021) that epistemic components are nonetheless required in the quantum setting. Finally, I consider how a recent proposal by Strevens (2021) meshes with an approach to initial conditions in statistical mechanics.

**David Wallace** (in-person)

Mellon Professor of History and Philosophy of Science, University of Pittsburgh.

*Thermodynamics with and without irreversibility*

Working within the control-theoretic framework for understanding thermodynamics, I develop a systematic way to characterize thermodynamic theories via their compatibility with various notions of coarse-graining, which can be thought of as parametrizing an agent’s degree of control of a system’s degrees of freedom, and explore the features of those theories. I consider the status of the Second Law in this framework, and distinguish two versions: the principle that entropy does not decrease, and the Kelvin/Clausius statements about the impossibility of transforming heat to work, or moving heat from a cold body to a hotter body, in a cyclic process. The former should be understood as relative to a coarse-graining, and can be violated given finer control than that coarse-graining permits; the latter is absolute, and binds any thermodynamic theory compatible with the laws of physics. I illustrate these points via a discussion of Maxwell’s demon.

**Nicole Yunger Halpern** (remote)

National Institute of Standards and Technology NIST and Joint Center for Quantum Information and Computer Science, University of Maryland

Physicists often study small systems that thermalize by exchanging quantities with large environments. The exchanged quantities—heat, particles, electric charge, etc.—are conserved globally, and the thermalization helps define time’s arrow. If quantum, the quantities are represented by Hermitian operators. We often assume that the operators commute, meaning that they represent quantities that can be simultaneously measured. Yet, it is non-commuting operators that underlie quantum phenomena such as uncertainty principles. What happens if thermodynamic conserved quantities don’t commute? This question, mostly overlooked for decades, came to light recently at the intersection of quantum information theory and thermodynamics (Majigy, Braasch, et al. 2023). Noncommutation of conserved thermodynamic quantities has been found to enhance entanglement (Majidy, Lasek, et al. 2023b), decrease entropy-production rates (Upadhaya et al. 2023), alter the eigenstate thermalization hypothesis (Murthy et al, 2023), and more. This growing subfield illustrates how 21st-century quantum information science is extending 19th-century thermodynamics.

[1] NYH, Faist, Oppenheim, and Winter, Nat. Comms.**7**, 12051 (2016). https:// www.nature.com/articles/ncomms12051 [2] Majidy, Braasch, Lasek, Upadhyaya, Kalev, and NYH, Nat. Rev. Phys. (2023). https://www.nature.com/articles/s42254-023-00641-9 [3] Majidy, Lasek, Huse, and NYH, Phys. Rev. B

**107**045102 (2023). https:// journals.aps.org/prb/abstract/10.1103/PhysRevB.107.045102 [4] Upadhyaya, Braasch, Landi, and NYH, arXiv:2305.15480 (2023). [5] Murthy, Babakhani, Iniguez, Srednicki, and NYH, Phys. Rev. Lett.

**130**, 140402 (2023). https://doi.org/10.1103/PhysRevLett.130.140402