Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1501.06545 · Physical Review Letters

Jarzynski Equality in PT -Symmetric Quantum Mechanics

Sebastian Deffner, Avadh Saxena

Published Apr 13, 2015• 73 citations
arXivHTMLPDF

Abstract

We show that the quantum Jarzynski equality generalizes to $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics with unbroken $\mathcal{P}\mathcal{T}$ symmetry. In the regime of broken $\mathcal{P}\mathcal{T}$ symmetry, the Jarzynski equality does not hold as also the $\mathcal{C}\mathcal{P}\mathcal{T}$ norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system---two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken $\mathcal{P}\mathcal{T}$ symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

DOI
10.1103/physrevlett.114.150601

Related papers

Quantum work relations and response theory in parity-time-symmetric quantum systems

Bo-Bo Wei

In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extends to a parity-time- (PT-) symmetric quantum system with unbroken PT symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory, and Onsager reciprocal relations for the PT-symmetric quantum system are recovered as special cases of the universal quantum work relation in a PT-symmetric quantum system. In the regime of broken PT symmetry, the universal quantum work relation does not hold because the norm is not preserved during the dynamics.

arXiv:1711.00586•Physical review. E•Jan 11, 2018•12 citations

Links between dissipation and Rényi divergences in PT -symmetric quantum mechanics

Bo-Bo Wei

Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary nonequilibrium process is related to the R\'enyi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to $\mathcal{PT}$-symmetric quantum mechanics with unbroken $\mathcal{PT}$ symmetry. In the regime of broken $\mathcal{PT}$ symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.

arXiv:1710.06059•Physical Review A•Jan 9, 2018•8 citations

Crooks fluctuation theorem in ${\mathscr{PT}}$-symmetric quantum mechanics

Meng Zeng, Ee Hou Yong

Following the recent work by Deffner and Saxena (2015 Phys. Rev. Lett. 114 150601), where the Jarzynski equality is generalised to non-Hermitian quantum mechanics, we prove in this work a stronger form of Jarzynski equality, the Crooks fluctuation theorem, also in the non-Hermitian formalism when the system is in the unbroken -symmetric phase.

Journal of Physics Communications•Sep 26, 2017•21 citations

Validity of non-Hermitian fluctuation theorem in open Quantum system with unbroken PT- symmetry

Saurov Hazarika

In a recent paper, Deffner and Saxena (2015 Phys. Rev. Lett. 114 150601) showed that quantum Jarzynski equality generalizes to PT- symmetric quantum mechanics with unbroken symmetry. later Zeng and Yong (2017 Journal of Phys. Commun. 1 031001) extended this work to Crook's fluctuation theorem. In another recent paper, Andrew Smith et al 2018 discusses non-equilibrium work relation in open quantum system. In this paper, we will discuss the validity of non-Hermitian fluctuation theorem in open quantum system, in a region of unbroken PT- symmetry.

arXiv:1808.08369•Aug 25, 2018•0 citations

Observation of PT phase transition in a simple mechanical system

Carl M. Bender, Bjorn K. Berntson, David Parker +1 more

If a quantum-mechanical Hamiltonian is PT symmetric, there are two possibilities: either all of the eigenvalues are real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else some of the eigenvalues are real and some are complex, in which case the Hamiltonian is said to be in a broken-PT-symmetric phase. As one varies the parameters of the Hamiltonian, one can pass through the phase transition that separates the unbroken and broken phases. This transition has recently been observed in a variety of laboratory experiments. This paper explains the phase transition in a simple and intuitive fashion and then describes an elementary experiment in which the phase transition is easily observed.

arXiv:1206.4972•American Journal of Physics•Feb 19, 2013•333 citations

Symmetry-Enforced Non-Hermitian Jarzynski Equality in an SU(2)-Rotated Family of Hybrid $\mathcal{PT}$--$\mathcal{APT}$ Systems

Zongru Yang, Teng Liu, Xiaodong Tan +2 more

The Jarzynski equality is a cornerstone of nonequilibrium thermodynamics, linking work statistics to equilibrium free-energy differences. Although it has been extensively verified in classical and quantum Hermitian settings, its status in non-Hermitian dynamics remains under debate. Here we show that, in a postselected no-quantum-jump framework, a conditional non-Hermitian Jarzynski equality holds when the transition probabilities obey a parity-exchange symmetry. We study a constructed family of two-level hybrid Hamiltonians formed as linear combinations of parity-time ($\mathcal{PT}$) and anti-parity-time ($\mathcal{APT}$) symmetric terms, and demonstrate using complementary geometric and algebraic arguments that the parity-exchange symmetry persists throughout the corresponding $\mathrm{SU}(2)$-rotated orbit. Relative to previous $\mathcal{PT}$-focused conditional Jarzynski equality results, the advance here is an extension of the symmetry criterion from the isolated $\mathcal{PT}$ endpoint to a broader $\mathcal{PT}$--$\mathcal{APT}$ hybrid family. Experimentally, we implement three representative points, $θ_k = 0, π/4, π/2$, in a single trapped $^{171}\mathrm{Yb}^+$ ion and measure the resulting work distributions under cyclic protocols with $ΔF = 0$, confirming the predicted symmetry criterion at those points. Our results establish a symmetry-based extension of the conditional non-Hermitian Jarzynski relation within this restricted two-level setting.

quant-pharXiv:2605.10099•May 12, 2026•0 citations
We show that the quantum Jarzynski equality generalizes to PT\mathcal{P}\mathcal{T}PT-symmetric quantum mechanics with unbroken PT\mathcal{P}\mathcal{T}PT symmetry. In the regime of broken PT\mathcal{P}\mathcal{T}PT symmetry, the Jarzynski equality does not hold as also the CPT\mathcal{C}\mathcal{P}\mathcal{T}CPT norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system---two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT\mathcal{P}\mathcal{T}PT symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.
In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extends to a parity-time- (PT-) symmetric quantum system with unbroken PT symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory, and Onsager reciprocal relations for the PT-symmetric quantum system are recovered as special cases of the universal quantum work relation in a PT-symmetric quantum system. In the regime of broken PT symmetry, the universal quantum work relation does not hold because the norm is not preserved during the dynamics.
Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary nonequilibrium process is related to the R\'enyi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to PT\mathcal{PT}PT-symmetric quantum mechanics with unbroken PT\mathcal{PT}PT symmetry. In the regime of broken PT\mathcal{PT}PT symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.
Crooks fluctuation theorem in PT{\mathscr{PT}}PT-symmetric quantum mechanics
In a recent paper, Deffner and Saxena (2015 Phys. Rev. Lett. 114 150601) showed that quantum Jarzynski equality generalizes to PT- symmetric quantum mechanics with unbroken symmetry. later Zeng and Yong (2017 Journal of Phys. Commun. 1 031001) extended this work to Crook's fluctuation theorem. In another recent paper, Andrew Smith et al 2018 discusses non-equilibrium work relation in open quantum system. In this paper, we will discuss the validity of non-Hermitian fluctuation theorem in open quantum system, in a region of unbroken PT- symmetry.
If a quantum-mechanical Hamiltonian is PT symmetric, there are two possibilities: either all of the eigenvalues are real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else some of the eigenvalues are real and some are complex, in which case the Hamiltonian is said to be in a broken-PT-symmetric phase. As one varies the parameters of the Hamiltonian, one can pass through the phase transition that separates the unbroken and broken phases. This transition has recently been observed in a variety of laboratory experiments. This paper explains the phase transition in a simple and intuitive fashion and then describes an elementary experiment in which the phase transition is easily observed.
Symmetry-Enforced Non-Hermitian Jarzynski Equality in an SU(2)-Rotated Family of Hybrid PT\mathcal{PT}PT--APT\mathcal{APT}APT Systems
The Jarzynski equality is a cornerstone of nonequilibrium thermodynamics, linking work statistics to equilibrium free-energy differences. Although it has been extensively verified in classical and quantum Hermitian settings, its status in non-Hermitian dynamics remains under debate. Here we show that, in a postselected no-quantum-jump framework, a conditional non-Hermitian Jarzynski equality holds when the transition probabilities obey a parity-exchange symmetry. We study a constructed family of two-level hybrid Hamiltonians formed as linear combinations of parity-time (PT\mathcal{PT}PT) and anti-parity-time (APT\mathcal{APT}APT) symmetric terms, and demonstrate using complementary geometric and algebraic arguments that the parity-exchange symmetry persists throughout the corresponding SU(2)\mathrm{SU}(2)SU(2)-rotated orbit. Relative to previous PT\mathcal{PT}PT-focused conditional Jarzynski equality results, the advance here is an extension of the symmetry criterion from the isolated PT\mathcal{PT}PT endpoint to a broader PT\mathcal{PT}PT--APT\mathcal{APT}APT hybrid family. Experimentally, we implement three representative points, θk=0,π/4,π/2θ_k = 0, π/4, π/2θk​=0,π/4,π/2, in a single trapped 171Yb+^{171}\mathrm{Yb}^+171Yb+ ion and measure the resulting work distributions under cyclic protocols with ΔF=0ΔF = 0ΔF=0, confirming the predicted symmetry criterion at those points. Our results establish a symmetry-based extension of the conditional non-Hermitian Jarzynski relation within this restricted two-level setting.