Carlo Sparaciari: Multi-resource theories and the first law

Carlos begins by expressing gratitude for the invitation to present at the conference. He introduces the collaborative work inspired by thermodynamics, which extends beyond traditional thermodynamics to explore a general resource theory. This theory aims to describe tasks involving multiple resources, such as quantum computation and thermodynamics with multiple conserved quantities. Carlos emphasizes the importance of resource theories in various physical scenarios and the need to consider multiple resources for a comprehensive understanding.

The speaker delves into the concept of single resource theories, explaining them as tools to describe an agent's perspective on transforming a system's state within certain operational constraints. He uses the example of Alice in a lab to illustrate the limitations and possibilities of state transformations. The paragraph discusses the classification of states into 'resourceful' and 'free' states, and introduces the notion of monotones in resource theories, which are functions that do not increase under allowed operations.

Carlos presents thermodynamics as an example of a resource theory with thermal operations. He describes the setting where an experimentalist has access to an infinite thermal bath and the allowed operations include taking ancillary systems from the bath, reversible operations preserving energy, and discarding parts of the system. The free states in this theory are thermal states at the same temperature as the reservoir, and the speaker introduces the concept of almost free energy as a monotone for this theory.

The speaker transitions to multi-resource theories by discussing the framework and the concept of reversibility. He explains that multi-resource theories are built by intersecting the allowed operations of different single-resource theories, each associated with different conservation laws and constraints. The paragraph also touches on the idea of invariant sets and the difference between invariance and being free in the context of multi-resource theories.

Carlos defines reversibility in the context of resource theories as a cyclic transformation that does not result in the loss of resources. He introduces the concept of batteries as additional systems that store specific kinds of resources and are used to quantify resources during transformations. The speaker also explains the asymptotic equivalence property, which is crucial for representing the state space and performing transformations between different states.

The speaker discusses the interconversion of resources within multi-resource theories, using the analogy of currency exchange at a bank. He explains the properties that characterize a 'bank' in multi-resource theory, such as the need for an exchange of resources, fixed exchange rates, and the stability of the bank's state during transformations. Carlos also introduces the concept of a 'bank monotone,' which determines the exchange rate for resource conversion.

Carlos applies the multi-resource theory framework to thermodynamics with many conserved quantities, describing the scenario where an isolated system interacts through reversible transformations. He explains how different resource theories can be combined, how banks are defined in this context, and how interconversion is performed using the bank and the associated bank monotone.

In conclusion, Carlos summarizes the framework introduced for multi-resource theories, its application to thermodynamics, and the potential for extending this framework to other resource theories. He suggests future research directions, such as finding general conditions for the asymptotic equivalence property, exploring the use of batteries in different resource theories, and considering the implications of non-commuting charges in multi-resource scenarios.

The final part of the script includes a Q&A session where the audience asks questions about the implications of the presented theory, its application to ordinary systems, and the interpretation of banks in multi-resource theories. Carlos addresses these questions, providing further insights into the theory's practical applications and theoretical underpinnings.