Fundamental limitations for quantum and nanoscale thermodynamics

By Michal Horodecki, Jonathan Oppenheim. Nature Communications, 2011

762 citations recorded by the source corpus.

The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit—when the number of particles becomes very large. Here we study thermodynamics in the opposite regime—at both the nanoscale and when quantum effects become important. Applying results from quantum information theory, we construct a theory of thermodynamics in these limits. We derive general criteria for thermodynamical state transitions, and, as special cases, find two free energies: one that quantifies the deterministically extractable work from a small system in contact with a heat bath, and the other that quantifies the reverse process. We find that there are fundamental limitations on work extraction from non-equilibrium states, owing to finite size effects and quantum coherences. This implies that thermodynamical transitions are generically irreversible at this scale. As one application of these methods, we analyse the efficiency of small heat engines and find that they are irreversible during the adiabatic stages of the cycle. The usual laws of thermodynamics that are valid for macroscopic systems do not necessarily apply to the nanoscale, where quantum effects become important. Here, the authors develop a theoretical framework based on quantum information theory to properly treat thermodynamics at the nanoscale.

Subfields: Civil and Structural Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f5ac15dc616172e4cb9f27703e57040aaeee6af3

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Citations in the corpus

Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, methodology): “The approach most suited to our needs in this work is the one followed in [21, 25, 27, 28], which has emerged from the theory of entanglement [20].”
The role of quantum coherence in non-equilibrium entropy production (2017, background): “[16] Horodecki, M.”
Quantum coherence, time-translation symmetry and thermodynamics (2014, background): “The question is now, how much quantum coherence can be preserved in this process? Here, we establish a lower bound on the guaranteed coherence for such a transformation that relies only on known results about thermodynamic transformations among incoherent states [4] and the convexity of the set of t”
A mathematical theory of resources (2014, neutral): “…operations (relative to a symmetry group G ) & a unitary rep’n of G nonuniformity [27, 25] Hilbert spaces noisy operations athermality [31, 13, 28] pairs of a Hilbert space T -thermal operations (relative to temperature T ) & a Hamiltonian Table 1: The resource theories of processes which…”
The role of quantum information in thermodynamics—a topical review (2015, background): “This constraint is easier to tackle mathematically, and the two resource theories induce the same pre-order on classical states, leading to a condition for state transformation called Gibbs-majorization (which is majorization after a rescaling of the eigenvalues) [87].”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “At the same time, further interconnections to thermal operations [92, 294, 395] and resource theory [394] will emerge by quantifying benefits and limits of heat-bath coupling [22] in terms of reachable sets.”
Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures (2015, background): “This study includes dynamical analysis of engines and refrigerators in the quantum regime [1,14,16–40], theoretical frameworks that take into account single-shot events [41,42], and the study of thermalization mechanisms [43–45].”