The resource theory of informational nonequilibrium in thermodynamics

Abstract

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.

Implications of Coupling in Quantum Thermodynamic Machines

“…As an example, the statement of the second law of thermodynamics in the presence of an ancilla [1,2] or, when the system has coherence [3,4], has been established in great details, from where the classical version of the second law emerges under appropriate limits. The study of thermodynamics in quantum domain can be approached from different directions such as information-theoretic point of view [5][6][7][8][9][10] or resource-theoretic aspect [11][12][13]. Another important constituent, in this area of study, is the work extraction from quantum systems [14][15][16][17][18].…”

Additional energy-information relations in thermodynamics of small systems

“…Analogously to thermodynamic resource theory [23][24][25], the regime of validity can be formulated in terms of allowed operations. Instead of giving a validity condition it is possible to restrict the set of allowed physical processes.…”

Toward Physical Realizations of Thermodynamic Resource Theories

“…Yet heat, work, and entropy characterize the few-particle scales that experimentalists can increasingly control (e.g., [23][24][25][26][27]), as well as single trials. Small scales have been described by TRTs (e.g., [2,[28][29][30][31][32][33]). These results fall under the umbrella of one-shot statistical mechanics, an application of the one-shot information theory that generalizes Shannon theory [34].…”

“…depends on the greatest probability p max in a distribution P or on the greatest eigenvalue p max of a quantum state ρ. H ∞ relates to the work that a TRT agent must invest to create a state (ρ, H) [2,29]. The work extractable from (ρ, H) relates to…”