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Fluctuating States: What is the Probability of a Thermodynamical Transition?

Alhambra, ÁM; Oppenheim, J; Perry, C; (2016) Fluctuating States: What is the Probability of a Thermodynamical Transition? Physical Review X , 6 (4) 10.1103/PhysRevX.6.041016. Green open access

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Abstract

If the second law of thermodynamics forbids a transition from one state to another, then it is still possible to make the transition happen by using a sufficient amount of work. But if we do not have access to this amount of work, can the transition happen probabilistically? In the thermodynamic limit, this probability tends to zero, but here we find that for finite-sized and quantum systems it can be finite. We compute the maximum probability of a transition or a thermodynamical fluctuation from any initial state to any final state and show that this maximum can be achieved for any final state that is block diagonal in the energy eigenbasis. We also find upper and lower bounds on this transition probability, in terms of the work of transition. As a by-product, we introduce a finite set of thermodynamical monotones related to the thermomajorization criteria which governs state transitions and compute the work of transition in terms of them. The trade-off between the probability of a transition and any partial work added to aid in that transition is also considered. Our results have applications in entanglement theory, and we find the amount of entanglement required (or gained) when transforming one pure entangled state into any other.

Type: Article
Title: Fluctuating States: What is the Probability of a Thermodynamical Transition?
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevX.6.041016
Publisher version: http://dx.doi.org/10.1103/PhysRevX.6.041016
Language: English
Additional information: Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License (https://creativecommons.org/licenses/by/3.0/0. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery.ucl.ac.uk/id/eprint/1532072
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