Carina Prunkl: Resource theories of thermodynamics and axiomatics: a comparison

The speaker expresses gratitude for the opportunity to participate in a conference that bridges philosophy and physics, focusing on resource theories and their connection to axiomatic thermodynamics. They highlight the importance of this interdisciplinary approach and set the stage for a discussion on how resource theories might provide new insights into fundamental physical principles, such as the second law of thermodynamics. The speaker also mentions the existence of prior work on the topic and their intention to compare and contrast these theories.

This paragraph delves into the specifics of axiomatic thermodynamics, which aims to establish a unique entropy function through a set of axioms. The speaker outlines the motivation behind this approach, emphasizing its pedagogical value and its goal to present equilibrium thermodynamics as an ideal physical theory with well-defined mathematical constructs. Key features of this approach include its focus on phenomenological entropy, macroscopic systems, and equilibrium states, as well as the notion of adiabatic accessibility, which is central to defining the order relation among states.

The speaker continues the discussion on axiomatic thermodynamics by detailing the axioms that lead to the establishment of a unique entropy function. These axioms include reflexivity, transitivity, consistency, scaling invariance, splitting and recombination, and stability. The paragraph also introduces the comparison hypothesis, which is a strong assumption that all pairs of states are comparable, and the entropy principle, which asserts the existence of a real-valued entropy function with specific properties.

Shifting focus to resource theories, the speaker outlines their three basic components: a set of free states, a restricted set of operations, and a set of resource states. The goal of resource theories is to determine the accessibility of states given these restrictions. The speaker also mentions a specific resource theory of noisy operations as an example and discusses how resource theories can be made structurally similar to axiomatic thermodynamics by imposing certain restrictions.

In this paragraph, the speaker compares the axiomatic approach with resource theories, noting the differences in their assumptions and motivations. While axiomatic thermodynamics is restrictive and focused on macroscopic systems, resource theories are more general and operational, including the concept of agents performing operations. The speaker also discusses the implications of these theories for understanding the second law of thermodynamics and the nature of entropy.

The speaker reflects on the philosophical puzzles surrounding thermodynamics, such as its universality and the nature of entropy. They quote Einstein and Peter Atkins to emphasize the broad applicability of thermodynamics and its relevance beyond traditional contexts. The speaker also raises questions about the interpretation of entropy and whether resource theories might suggest an information-theoretic view of entropy.

This paragraph explores the various interpretations of entropy, from being a measure of disorder to a property of microstates or macrostates. The speaker discusses the challenges in pinning down a single definition of entropy and whether resource theories might indicate an information-theoretic interpretation. They also question whether the success of resource theories in the context of information theory commits us to such a view of entropy.

The speaker examines the means-relative approach to thermodynamics, which considers practical impossibilities and the role of agents with varying knowledge or means. They argue that this approach does not necessarily commit us to an epistemic or information-theoretic view of entropy, as entropy can be seen as a property of the macro state, independent of the knowledge of individual agents.

In this paragraph, the speaker uses the example of assigning entropy to the Sun to illustrate the limitations of the means-relative and control-theoretic approaches. They suggest that these approaches may not fully capture the essence of thermodynamics when applied to objects like the Sun, where our ability to manipulate or control is limited, and question whether this implies a commitment to an information-theoretic understanding of entropy.

The speaker concludes by summarizing their main points, emphasizing that resource theories are powerful for predicting state transitions and capturing the control-theoretic aspect of thermodynamics. They express skepticism about the means-relative approach and its implications for the understanding of entropy. The speaker also raises open questions about the universality of thermodynamics and whether resource theories can provide new insights into this phenomenon.

In the final paragraph, the speaker encourages further discussion on the topics presented, acknowledging that there are differing views and open questions. They highlight the broad applicability of resource theories beyond information theory, using the example of geometric constructions in mathematics, and reiterate their skepticism about the commitment to an information-theoretic view of entropy.