To what extent is the resource theory approach to thermodynamics relevant for realistic experimental scenarios? We deconstruct this framework, showing that each transition among incoherent states allowed in the theory can be obtained by sequentially applying elementary thermal operations. These only couple the bath to single transitions in the system and satisfy detailed balance. We show that most of them can be realised within one of the simplest thermodynamic models, a resonant Jaynes-Cummings interaction with a single mode bosonic bath, and discuss the link to thermalisation models. No external control of the Hamiltonian or ancillae are needed. We also present an extension of Birkhoff's theorem for bistochastic matrices to thermodynamics, and discuss its consequences for the problem of simulating arbitrary thermal processes. Finally, we show that the constraints found within thermal operations for transitions among incoherent states are to a large extent \emph{universal}, i.e. they apply to a broad class consisting of very different thermodynamic frameworks.
To what extent is the resource theory approach to thermodynamics relevant for realistic experimental scenarios? We deconstruct this framework, showing that each transition among incoherent states allowed in the theory can be obtained by sequentially applying elementary thermal operations. These only couple the bath to single transitions in the system and satisfy detailed balance. We show that most of them can be realised within one of the simplest thermodynamic models, a resonant Jaynes-Cummings interaction with a single mode bosonic bath, and discuss the link to thermalisation models. No external control of the Hamiltonian or ancillae are needed. We also present an extension of Birkhoff's theorem for bistochastic matrices to thermodynamics, and discuss its consequences for the problem of simulating arbitrary thermal processes. Finally, we show that the constraints found within thermal operations for transitions among incoherent states are to a large extent \emph{universal}, i.e. they apply to a broad class consisting of very different thermodynamic frameworks.
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.
To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show that this theory is well reproduced by a Jaynes-Cummings interaction in rotating wave approximation and draw a connection to standard descriptions of thermalisation. We then prove that elementary thermal operations present tighter constraints on the allowed transformations than thermal operations. Mathematically, this illustrates the failure at finite temperature of fundamental theorems by Birkhoff and Muirhead-Hardy-Littlewood-Polya concerning stochastic maps. Physically, this implies that stronger constraints than those imposed by single-shot quantities can be given if we tailor a thermodynamic resource theory to the relevant experimental scenario. We provide new tools to do so, including necessary and sufficient conditions for a given change of the population to be possible. As an example, we describe the resource theory of the Jaynes-Cummings model. Finally, we initiate an investigation into how our resource theories can be applied to Heat Bath Algorithmic Cooling protocols.
We develop a resource-theoretic framework that allows one to bridge the gap between two approaches to quantum thermodynamics based on Markovian thermal processes (which model memoryless dynamics) and thermal operations (which model arbitrarily non-Markovian dynamics).Our approach is built on the notion of memory-assisted Markovian thermal processes, where memoryless thermodynamic processes are promoted to non-Markovianity by explicitly modeling ancillary memory systems initialized in thermal equilibrium states.Within this setting, we propose a family of protocols composed of sequences of elementary two-level thermalizations that approximate all transitions between energy-incoherent states accessible via thermal operations.We prove that, as the size of the memory increases, these approximations become arbitrarily good for all transitions in the infinite temperature limit, and for a subset of transitions in the finite temperature regime.Furthermore, we present solid numerical evidence for the convergence of our protocol to any transition at finite temperatures.We also explain how our framework can be used to quantify the role played by memory effects in thermodynamic protocols such as work extraction.Finally, our results show that elementary control over two energy levels at a given time is sufficient to generate all energy-incoherent transitions accessible via thermal operations if one allows for ancillary thermal systems.
Thermal operations are quantum channels that play a central role in deriving thermodynamic limitations in quantum systems. However, they were originally defined by implementation procedures rather than by fundamental principles. Alternative models of thermal processes have been proposed, but they obscure the resources required for implementation. Here, we identify the universal principle that separates these models. We show that thermal operations are uniquely characterized by a purely quantum information-theoretic property, which we call informational equilibrium. This formulation does not assume a particular Hamiltonian or even a notion of temperature: a channel is a thermal operation precisely when it leaves its environment invariant whenever the system is prepared in equilibrium. In this way, the usual energetic description of equilibrium (i.e., Gibbs states) emerges as a representation of an underlying informational constraint. Extending this framework, we note that enforcing environment invariance for all system inputs leads to catalytic channels, which idealize perfectly reusable heat baths. This informational equilibrium perspective culminates in a hierarchy for doubly-stochastic quantum channels, with strict separations between the classes. Our refined hierarchy sharpens the failure of the Birkhoff-von Neumann theorem in the quantum regime, and highlights the richer structural landscape of quantum channels compared to classical stochastic processes that cannot be captured by state-convertibility relations.
Thermal operations are a generic description for allowed state transitions under thermodynamic restrictions. However, the quest for simpler methods to encompass all these processes remains unfulfilled. We resolve this challenge through the catalytic use of thermal baths, which are assumed to be easily accessible. We select two sets of simplified operations: elementary thermal operations and Markovian thermal operations. They are known for their experimental feasibility, but fail to capture the full extent of thermal operations due to their innate Markovianity. We nevertheless demonstrate that this limitation can be overcome when the operations are enhanced by ambient-temperature Gibbs state catalysts. In essence, our result indicates that free states within thermal operations can act as catalysts that provide the necessary non-Markovianity for simpler operations. Furthermore, we prove that when any catalyst can be employed, different thermal processes (thermal operations, elementary thermal operations, and Markovian thermal operations) converge. Notably, our results extend to scenarios involving initial states with coherence in the energy eigenbasis, a notoriously difficult process to characterise.
The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies.