Thermodynamics imposes fundamental constraints on the evolution of quantum systems. These constraints and their dynamical consequences have been formulated within distinct paradigms, including axiomatic approaches based on quantum master equations, microscopic descriptions of open-system dynamics, and operational formulations rooted in resource theories. While each perspective has yielded important insights into thermodynamically consistent quantum dynamics, their precise relationship has remained unresolved. Here we establish the exact equivalence of these three paradigms in the Markovian regime. We prove that thermal Lindbladians satisfying Markovianity, time-translation symmetry, and quantum detailed balance are precisely those admitting a microscopic realisation as an energy-conserving thermal collision model and, equivalently, those generating Markovian thermal operations. This unifies the existing approaches to Markovian quantum thermodynamics and identifies its dynamical underpinnings. We further provide an explicit microscopic protocol for simulating thermal Markovian processes with controlled finite-time simulation errors. We illustrate its applicability by providing faithful thermal collision-model implementations of a qubit thermalising in a bosonic environment and of a three-level autonomous thermal machine. In the latter case, the protocol gives rise to a finite-stroke thermal engine that not only reproduces the continuous-time dynamics but also its steady-state thermodynamic performance. As a whole, these results establish a unified foundation for Markovian quantum thermodynamics, showing that its axiomatic, microscopic, and operational formulations are exactly equivalent and providing a universal protocol for implementing thermal processes and machines.Thermodynamics imposes fundamental constraints on the evolution of quantum systems. These constraints and their dynamical consequences have been formulated within distinct paradigms, including axiomatic approaches based on quantum master equations, microscopic descriptions of open-system dynamics, and operational formulations rooted in resource theories. While each perspective has yielded important insights into thermodynamically consistent quantum dynamics, their precise relationship has remained unresolved. Here we establish the exact equivalence of these three paradigms in the Markovian regime. We prove that thermal Lindbladians satisfying Markovianity, time-translation symmetry, and quantum detailed balance are precisely those admitting a microscopic realisation as an energy-conserving thermal collision model and, equivalently, those generating Markovian thermal operations. This unifies the existing approaches to Markovian quantum thermodynamics and identifies its dynamical underpinnings. We further provide an explicit microscopic protocol for simulating thermal Markovian processes with controlled finite-time simulation errors. We illustrate its applicability by providing faithful thermal collision-model implementations of a qubit thermalising in a bosonic environment and of a three-level autonomous thermal machine. In the latter case, the protocol gives rise to a finite-stroke thermal engine that not only reproduces the continuous-time dynamics but also its steady-state thermodynamic performance. As a whole, these results establish a unified foundation for Markovian quantum thermodynamics, showing that its axiomatic, microscopic, and operational formulations are exactly equivalent and providing a universal protocol for implementing thermal processes and machines.

quant-pharXiv:2607.15376Jul 20, 20260 citations

Microscopic Description: Non-Markovian Case

́Angel Rivas, Susana F. Huelga

SpringerBriefs in physicsSep 29, 20111 citation

Emergent Non-Markovian Nonlinear Qubit From Collective Spin Interactions

Gregory T. Carroll, Michael R. Geller, Andre Erpenbeck

Open-system descriptions are typically introduced by coupling a quantum system to an external environment. Here we show that a closed interacting many-body system can itself generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit through finite-size corrections to a nonlinear mean-field limit. We demonstrate this using the Kitagawa-Ueda one-axis twisting model, $H=χJ_z^2$ , a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large- $N$ regime of this model has been extensively studied, the conventional fixed- $χ$ scaling does not yield a nontrivial dynamical large- $N$ limit. In this paper, we investigate a complementary large- $N$ formulation obtained from the double limit $N\rightarrow\infty$ and $χ\rightarrow O(g/N)$ , where $g$ is a coupling constant. We derive the leading finite- $N$ corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale $t_\varphi\geq\sqrt{N}/(2g)$ . Exact finite- $N$ calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.Open-system descriptions are typically introduced by coupling a quantum system to an external environment. Here we show that a closed interacting many-body system can itself generate a controlled non-Markovian quantum channel acting on a reduced nonlinear qubit through finite-size corrections to a nonlinear mean-field limit. We demonstrate this using the Kitagawa-Ueda one-axis twisting model, $H=χJ_z^2$, a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large-$N$ regime of this model has been extensively studied, the conventional fixed-$χ$ scaling does not yield a nontrivial dynamical large-$N$ limit. In this paper, we investigate a complementary large-$N$ formulation obtained from the double limit $N\rightarrow\infty$ and $χ\rightarrow O(g/N)$, where $g$ is a coupling constant. We derive the leading finite-$N$ corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale $t_\varphi\geq\sqrt{N}/(2g)$. Exact finite-$N$ calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.

quant-pharXiv:2608.07723Aug 11, 20260 citations

Probabilities and microscopic behaviors

Keith S. Stowe

Cambridge University Press eBooksMay 10, 20070 citations

Exploring a strongly non-Markovian behavior

Vasyl A. Alba, Gordon J Berman, William Bialek +1 more

Bulletin of the American Physical SocietyMar 15, 20170 citations

Why quantum dynamics can be formulated as a Markov process

Piotr Garbaczewski, Robert Olkiewicz

We invert the well-developed strategy of studying dynamics in terms of probability densities and investigate the problem of the most likely microscopic propagation scenario, which is consistent with the given priori (possibly phenomenological) input-output statistics data for the process taking place in a finite-time interval. A solution of this so-called Schr\"odinger problem is known to provide an adequate probabilistic framework for the measure preserving dynamics which is Markovian. We pay particular attention to the subclass of nonstationary solutions, determined by unitary-wave-packet evolution (Schr\"odinger wave mechanics). The existence of the pertinent Markovian diffusion is known on general grounds, but no explicit demonstration (through detailed computational arguments) until now was available even in the simplest cases. We give a definitive probabilistic description of the free quantum dynamics as a stochastic process solving Schr\"odinger's interpolation problem. The Markov diffusion arised as a particular case singled out by a suitable Feynman-Kac semigroup.We invert the well-developed strategy of studying dynamics in terms of probability densities and investigate the problem of the most likely microscopic propagation scenario, which is consistent with the given priori (possibly phenomenological) input-output statistics data for the process taking place in a finite-time interval. A solution of this so-called Schr\"odinger problem is known to provide an adequate probabilistic framework for the measure preserving dynamics which is Markovian. We pay particular attention to the subclass of nonstationary solutions, determined by unitary-wave-packet evolution (Schr\"odinger wave mechanics). The existence of the pertinent Markovian diffusion is known on general grounds, but no explicit demonstration (through detailed computational arguments) until now was available even in the simplest cases. We give a definitive probabilistic description of the free quantum dynamics as a stochastic process solving Schr\"odinger's interpolation problem. The Markov diffusion arised as a particular case singled out by a suitable Feynman-Kac semigroup.

Physical Review AMay 1, 199519 citations

H=χJ_z^2

, a paradigmatic model of collective spin dynamics, spin squeezing, and two-component Bose-Einstein condensates. Although the large-

N

regime of this model has been extensively studied, the conventional fixed-

χ

scaling does not yield a nontrivial dynamical large-

N

limit. In this paper, we investigate a complementary large-

N

formulation obtained from the double limit

N\rightarrow\infty

and

χ\rightarrow O(g/N)

, where

g

is a coupling constant. We derive the leading finite-

N

corrections to this limit and show that they correspond to an emergent non-Markovian dephasing process, producing a Gaussian decay of the Bloch-vector coherence with characteristic timescale

t_\varphi\geq\sqrt{N}/(2g)

. Exact finite-

N

calculations demonstrate that this effective open-system description becomes quantitatively accurate for systems containing on the order of one hundred qubits. The resulting framework provides a microscopic realization of non-Markovian dephasing generated intrinsically by a closed many-body system and enables efficient simulation of collective quantum dynamics beyond unitary mean-field theory. These results link the long-studied phenomenon of phase diffusion in atomic ensembles and Bose-Einstein condensates to the growing effort to characterize non-Markovian, beyond-Lindblad noise in quantum computing hardware, providing a rare case in which such a noise channel is derived from microscopic dynamics rather than fit phenomenologically.