Resource-theory models for thermodynamics

The resource-theory framework is a mathematical toolkit developed in quantum information theory. The framework models transformations—of quantum states or probability distributions—under restricted classes of operations. Thermodynamics constrains operations to conserve energy. An agent may access easily only states thermal relative to the ambient temperature. Athermal states can carry more information than thermal states do, more accessible energy, and/or more coherence relative to the energy eigenbasis. These properties serve as resources in thermodynamic tasks. For example, work may be extracted from a bath hotter than the environment, via a heat engine. Thermodynamic resource theories (TRTs) are used to quantify athermal states’ value. Quantification measures include "one-shot" entropies beyond the Shannon, von Neumann, and relative entropies. TRTs extend to quantum systems that exchange conserved charges, analogous to heat and particles, that fail to commute. This talk will overview TRTs. The framework stretches statistical mechanics beyond equilibrium, to small (e.g., three-level) systems, to coherent quantum states, and to noncommuting charges.