Beyond heat baths II: framework for generalized thermodynamic resource theories

Abstract

Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories. Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family's structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd's engine and Landauer's Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories' potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.

Quantum resource theories

“…when a given system interacts with a bath. Here we describe the resource theory of athermality, which involves just energy conservation, but its generalization to other conserved observables follows analogously (Gour et al, 2018c;Yunger Halpern, 2018;Yunger Halpern and Renes, 2016), including non-commuting observables (Guryanova et al, 2016;Halpern et al, 2016;Lostaglio et al, 2017). One begins by characterizing a physical system not only by its underlying Hilbert space H, but also by its Hamiltonian, since this corresponds to the property being conserved.…”

One-Shot Operational Quantum Resource Theory

“…Unlike the asymptotic theory (the limit of infinite i.i.d. copies) [21], only a few resource-specific results about entanglement [44,45], coherence [46][47][48], and (generalized) quantum thermodynamics [14,[49][50][51][52] (and magic states in a very recent work [53]) are known. Here we consider two important classes of free operations easily characterized by the theory of resource destroying (RD) maps [25]: the maximal free operations (e.g.…”

Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges

“…We recover the state (1) via several approaches, demonstrating its physical importance. We address puzzles raised in refs 21 , 27 about how to formulate a resource theory in which thermodynamic charges fail to commute. Closely related, independent work was performed by Guryanova et al.…”

“…Heat exchanges with a bath are modelled with ‘free states' and ‘free operations' 15 16 17 18 . These resource theories have been extended to model exchanges of additional physical quantities, such as particles and angular momentum 18 19 20 21 22 .…”