The resource theory of informational nonequilibrium in thermodynamics

By Gilad Gour, Markus P. Muller, Varun Narasimhachar, Robert W. Spekkens, Nicole Yunger Halpern. 2013

424 citations recorded by the source corpus.

We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degenerate). In this case, the only free operations are those that add noise to the system (or implement a reversible evolution) and the only nonequilibrium states are states of informational nonequilibrium, that is, states that deviate from the maximally mixed state. The degree of this deviation we call the state’s nonuniformity; it is the resource of interest here, the fuel that is consumed, for instance, in an erasure operation. We consider the different types of state conversion: exact and approximate, single-shot and asymptotic, catalytic and noncatalytic. In each case, we present the necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves. We also review the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies, and that of quantifying the gap between the nonuniformity one must expend to achieve a single-shot state preparation or state conversion and the nonuniformity one can extract in the reverse operation. Quantum state-conversion problems in this resource theory can be shown to be always reducible to their classical counterparts, so that there are no inherently quantum-mechanical features arising in such problems. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/007cca78221cf54a56d1c4acd76fb3fb70160e31

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In Statistical and Nonlinear Physics

Citations in the corpus

Second law of quantum complexity (2017, background): “An entropy gap, namely the difference between the entropy of a system and the maximum entropy in thermal equilibrium, is a resource [30].”
Quantum coherence and geometric quantum discord (2017, background): “…but can also provides the basis for its potential applications in a wide variety of promising subjects, such as quantum thermodynamics (Gour et al., 2015; Lostaglio et al., 2015a,b; Narasimhachar and Gour, 2015), reference frames (Bartlett et al., 2007), and quantum biology (Lambert et al., 2013).”
A mathematical theory of resources (2014, neutral): “The quantum resource theory of nonuniformity [27, 25] is deﬁned in terms of the following partitioned process theory.”
Quantum resource theories (2018, background): “Yet, the two operational classes have the same conversion power since one density matrix can be converted to another by noisy operations if and only if the conversion can be achieved by a unital channel (Gour et al., 2015b).”
Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions (2016, background): “The setup is also close to resource theoretic formulations of thermodynamics, in which one investigates which system transformations are possible given a set of freely available states and resources (all other states) [38,39].”
Macroscopic quantum states: Measures, fragility, and implementations (2017, background): “…has been a trend to formalize certain aspects of quantum mechanics such as entanglement (Horodecki et al., 2009), athermality (Goold et al., 2016; Gour et al., 2015), asymmetry (Gour and Spekkens, 2008) and coherence (Baumgratz et al., 2014; Marvian and Spekkens, 2016; Yadin et al., 2016) in the…”
The role of quantum information in thermodynamics—a topical review (2015, background): “In that case ; r s  monotones for this setting are called Schur monotone functions, of which information-theoretical entropy measures are examples [78, 80–83].”