David Wallace: Thermodynamics as control theory

The session begins with Joe Brown welcoming everyone and introducing the first speaker, David Wallace. Wallace acknowledges his absence from the previous session and aims to provide a brief recap of key points discussed, focusing on thermodynamics and its relation to other dynamic theories. He explains the concept of state spaces and dynamics, and how these relate to theories at different levels. He also mentions the limitations of thermodynamics when viewed from a dynamical perspective.

Wallace introduces the idea of thermodynamics as a control theory, where the focus is on external interventions and transformations rather than spontaneous system evolutions. He contrasts this with the traditional view of reduction in dynamic theories. Wallace proposes that understanding thermodynamics through control operations and external resources can offer new insights into the nature of thermodynamic systems and their transformations.

Wallace delves into the specifics of control operations, explaining how they map states to states and the importance of energy conservation in these processes. He discusses the maximum work that can be extracted from a system and introduces the concept of canonical states and Gibbs entropy. Wallace also touches on the similarities between classical and quantum mechanics in this context.

Addressing concerns in the foundations of statistical mechanics, Wallace argues that characterizing systems by probability distributions is valid for his purposes. He discusses the implications of using probability distributions in both classical and quantum mechanics and how these relate to control operations and energy extraction. Wallace emphasizes the practical aspects of control operations over theoretical concerns about probability interpretation.

Wallace explores the concept of combining systems and the resulting free energy that can be extracted. He explains how to calculate the free energy of a combined system and introduces the notion of thermal mixing. Wallace uses these ideas to illustrate the constraints on energy extraction even with perfect control operations, highlighting the Carnot efficiency limit.

Wallace introduces the idea of coarse graining in control theory, where interventions are limited to coarse-grained details of states. He formalizes the concept of coarse graining and explains its implications for control operations and energy extraction. Wallace discusses how coarse graining affects the entropy and free energy of a system, and the constraints it imposes on control operations.

Wallace elaborates on the concept of forward compatibility in control theories, where control operations must commute with coarse graining. He explains how this framework ensures that transformations are insensitive to fine-grained details. Wallace uses examples like spin echo experiments to illustrate forward compatibility and its implications for thermodynamic processes.

Wallace discusses how coarse grained entropy is defined and its relationship to control operations. He explains that coarse grained entropy is non-decreasing under control operations, and how this impacts the available free energy. Wallace illustrates these concepts with examples of different types of coarse graining, such as equilibration and Boltzmann coarse graining.

Wallace explores how knowledge of a system's macro state can be used to extract free energy. He explains that knowing the macro state allows for reversible transformations to lower energy states, thus maximizing work extraction. Wallace contrasts this with situations where only coarse grained control is possible, limiting the available free energy.

Wallace addresses the concept of Maxwell's demon within the control theory framework. He distinguishes between demons that can reduce coarse-grained entropy and those that can violate the Carnot limit. Wallace argues that while demons of the first kind can challenge certain interpretations of entropy, demons of the second kind are impossible due to the fundamental constraints of reversible thermodynamics.

Wallace discusses how control operations introduce irreversibility in thermodynamics. He explains that the direction of time in thermodynamics arises from constraints on control operations and coarse graining. Wallace highlights the importance of initial state considerations and how they influence the applicability of control theories to real systems.

Wallace elaborates on the importance of initial states in ensuring forward compatibility of control operations. He explains that initial states must lack fine-grained structures that could disrupt coarse graining assumptions. Wallace uses analogies from statistical mechanics to illustrate how initial state conditions play a crucial role in thermodynamic control theories.

Wallace discusses the practical implications of coarse graining and control theory in thermodynamics. He explains how different types of coarse graining maps reflect actual dynamical restrictions and how these influence control operations. Wallace emphasizes the importance of understanding these constraints to effectively apply thermodynamic control theory.

Wallace briefly touches on the extension of control theory concepts to quantum mechanics. He discusses how unitary transformations and energy preservation in quantum systems align with the control theory framework. Wallace suggests that coarse graining and control theory can provide a unified approach to understanding thermodynamics in both classical and quantum contexts.

Wallace wraps up his talk by summarizing key points about thermodynamics as a control theory. He emphasizes the importance of coarse graining, forward compatibility, and initial state considerations in this framework. Wallace suggests that this approach offers a robust way to understand thermodynamic irreversibility and the constraints on energy extraction, providing a foundation for future research.