Irreversible effects of random unitary transformations on coherence

A single spin that is misaligned with respect to the static external magnetic field is investigated as a toy model to clarify the nature of irreversibility in terms of inner friction and irreversible work. The coherence generation and the effects of unwanted transitions are analyzed in detail. The behavior of inner friction and irreversible work as a function of protocol time are analyzed for a finite-time unitary transformation. The coherence generation is shown to be the common sign for the inner friction and irreversible work. The excess energy sourced by the unwanted transitions for a quasistatic transformation is found to be the only sign for irreversible work. The angle The angle dependencies of the inner friction and irreversible work are also analyzed explicitly. The selected model and the considered realistic parameters are available to be implemented for the finite-time operations on the nuclear magnetic resonance setups.A single spin that is misaligned with respect to the static external magnetic field is investigated as a toy model to clarify the nature of irreversibility in terms of inner friction and irreversible work. The coherence generation and the effects of unwanted transitions are analyzed in detail. The behavior of inner friction and irreversible work as a function of protocol time are analyzed for a finite-time unitary transformation. The coherence generation is shown to be the common sign for the inner friction and irreversible work. The excess energy sourced by the unwanted transitions for a quasistatic transformation is found to be the only sign for irreversible work. The angle The angle dependencies of the inner friction and irreversible work are also analyzed explicitly. The selected model and the considered realistic parameters are available to be implemented for the finite-time operations on the nuclear magnetic resonance setups.

Sakarya University Journal of ScienceMay 10, 20210 citations

Probabilistic Coherence Transformation Under Strictly Incoherent Operation

Ao-Xiang Liu, Cong‐Feng Qiao

Jan 1, 20250 citations

Effective approach to open systems with probability currents and the Grothendieck formalism

Apostol Vourdas

An effective approach to open systems and irreversible phenomena is presented, where an open system $Σ(d)$ with $d$ -dimensional Hilbert space, is a subsystem of a larger isolated system $Σ(2d)$ (the `full universe') with $2d$ -dimensional Hilbert space. A family of Bargmann-like representations (called $z$ -Bargmann representations) introduces naturally the larger space. The $z$ -Bargmann representations are defined through semi-unitary matrices (which are a coherent states formalism in disguise). The `openness' of the system is quantified with the probability current that flows from the system to the external world. The Grothendieck quantity ${\cal Q}$ is shown to be related to the probability current, and is used as a figure of merit for the `openness' of a system. ${\cal Q}$ is expressed in terms of `rescaling transformations' which change not only the phase but also the absolute value of the wavefunction, and are intimately linked to irreversible phenomena (e.g., damping/amplification). It is shown that unitary transformations in the isolated system $Σ(2d)$ (full universe), reduce to rescaling transformations when projected to its open subsystem $Σ(d)$ . The values of the Grothendieck ${\cal Q}$ for various quantum states in an open system, are compared with those for their counterpart states in an isolated system.An effective approach to open systems and irreversible phenomena is presented, where an open system $Σ(d)$ with $d$-dimensional Hilbert space, is a subsystem of a larger isolated system $Σ(2d)$ (the `full universe') with $2d$-dimensional Hilbert space. A family of Bargmann-like representations (called $z$-Bargmann representations) introduces naturally the larger space. The $z$-Bargmann representations are defined through semi-unitary matrices (which are a coherent states formalism in disguise). The `openness' of the system is quantified with the probability current that flows from the system to the external world. The Grothendieck quantity ${\cal Q}$ is shown to be related to the probability current, and is used as a figure of merit for the `openness' of a system. ${\cal Q}$ is expressed in terms of `rescaling transformations' which change not only the phase but also the absolute value of the wavefunction, and are intimately linked to irreversible phenomena (e.g., damping/amplification). It is shown that unitary transformations in the isolated system $Σ(2d)$ (full universe), reduce to rescaling transformations when projected to its open subsystem $Σ(d)$. The values of the Grothendieck ${\cal Q}$ for various quantum states in an open system, are compared with those for their counterpart states in an isolated system.

arXiv:2509.07882Sep 9, 20250 citations

Coherence and randomness in quantum theory

Claude D. George, I. Prigogine

Physica A Statistical Mechanics and its ApplicationsDec 1, 197918 citations

Effective approach to open systems with probability currents and the Grothendieck formalism

Apostol Vourdas

An effective approach to open systems and irreversible phenomena is presented, where an open system Σ ( d ) with d -dimensional Hilbert space, is a subsystem of a larger isolated system Σ ( 2 d ) (the ‘full universe’) with 2 d -dimensional Hilbert space. A family of Bargmann-like representations (called z -Bargmann representations) introduces naturally the larger space. The z -Bargmann representations are defined through semi-unitary matrices (which are a coherent states formalism in disguise). The ‘openness’ of the system is quantified with the probability current that flows from the system to the external world. The Grothendieck quantity Q is shown to be related to the probability current, and is used as a figure of merit for the ‘openness’ of a system. Q is expressed in terms of ‘rescaling transformations’ which change not only the phase but also the absolute value of the wavefunction, and are intimately linked to irreversible phenomena (e.g., damping/amplification). It is shown that unitary transformations in the isolated system Σ ( 2 d ) (full universe), reduce to rescaling transformations when projected to its open subsystem Σ ( d ) . The values of the Grothendieck Q for various quantum states in an open system, are compared with those for their counterpart states in an isolated system.An effective approach to open systems and irreversible phenomena is presented, where an open system Σ ( d ) with d -dimensional Hilbert space, is a subsystem of a larger isolated system Σ ( 2 d ) (the ‘full universe’) with 2 d -dimensional Hilbert space. A family of Bargmann-like representations (called z -Bargmann representations) introduces naturally the larger space. The z -Bargmann representations are defined through semi-unitary matrices (which are a coherent states formalism in disguise). The ‘openness’ of the system is quantified with the probability current that flows from the system to the external world. The Grothendieck quantity Q is shown to be related to the probability current, and is used as a figure of merit for the ‘openness’ of a system. Q is expressed in terms of ‘rescaling transformations’ which change not only the phase but also the absolute value of the wavefunction, and are intimately linked to irreversible phenomena (e.g., damping/amplification). It is shown that unitary transformations in the isolated system Σ ( 2 d ) (full universe), reduce to rescaling transformations when projected to its open subsystem Σ ( d ) . The values of the Grothendieck Q for various quantum states in an open system, are compared with those for their counterpart states in an isolated system.

Annals of PhysicsSep 4, 20251 citation

An effective approach to open systems and irreversible phenomena is presented, where an open system

Σ(d)

with

d

-dimensional Hilbert space, is a subsystem of a larger isolated system

Σ(2d)

(the `full universe') with

2d

-dimensional Hilbert space. A family of Bargmann-like representations (called

z

-Bargmann representations) introduces naturally the larger space. The

z

-Bargmann representations are defined through semi-unitary matrices (which are a coherent states formalism in disguise). The `openness' of the system is quantified with the probability current that flows from the system to the external world. The Grothendieck quantity

{\cal Q}

is shown to be related to the probability current, and is used as a figure of merit for the `openness' of a system.

{\cal Q}

is expressed in terms of `rescaling transformations' which change not only the phase but also the absolute value of the wavefunction, and are intimately linked to irreversible phenomena (e.g., damping/amplification). It is shown that unitary transformations in the isolated system

Σ(2d)

(full universe), reduce to rescaling transformations when projected to its open subsystem

Σ(d)

. The values of the Grothendieck

{\cal Q}

for various quantum states in an open system, are compared with those for their counterpart states in an isolated system.