We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments.First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms.Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics.Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin.We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.
We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments.First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms.Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics.Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin.We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.
We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone.
We study the quantum conditional entropy production, which quantifies the irreversibly conditioned on the coupling memory of the system. We prove that the quantum unconditional entropy production is less than the conditional one, where the latter has contribution from the informational nonequilibriumness. The mismatch, defined as the quantum dissipative information, pinpoints the distributive correlation established between the environment and the memory. Although the quantum unconditional entropy production can be zero, the conditional one is in general not, which is beyond the thermal equilibrium. Positive quantum dissipative information characterizes a potential work waste. We also prove the quantum fluctuation theorems related to the conditional entropy production, based on different two-point measurement schemes. The dissipative information itself also follows the quantum fluctuation theorem. We present examples based on the qubit collisional model and the qubit Maxwell's demon.
Abstract Thermodynamic irreversibility is well characterized by the entropy production arising from non-equilibrium quantum processes. We show that the entropy production of a quantum system undergoing open-system dynamics can be formally split into a term that only depends on population unbalances, and one that is underpinned by quantum coherences. This allows us to identify a genuine quantum contribution to the entropy production in non-equilibrium quantum processes. We discuss how these features emerge both in Lindblad-Davies differential maps and finite maps subject to the constraints of thermal operations. We also show how this separation naturally leads to two independent entropic conservation laws for the global system-environment dynamics, one referring to the redistribution of populations between system and environment and the other describing how the coherence initially present in the system is distributed into local coherences in the environment and non-local coherences in the system-environment state. Finally, we discuss how the processing of quantum coherences and the incompatibility of non-commuting measurements leads to fundamental limitations in the description of quantum trajectories and fluctuation theorems.
Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.
We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the notion of entropy production in thermodynamics is extended to the quantum regime. Our result shows that the fluctuation theorems, which are normally considered for thermodynamic processes, can be a powerful tool to study the detailed statistics of quantum systems as well as the effect of coherence transfer in an arbitrary non-equilibrium quantum process. We introduce a complex-valued entropy production to fully understand the relation between the forward and backward processes through the quantum channel. We find the physical meaning of the imaginary part of entropy production to witness the broken symmetry of the quantum channel. We also show that the imaginary part plays a crucial role in deriving the second law from the quantum fluctuation theorem. The dissipation and fluctuation of various quantum resources including quantum free energy, asymmetry and entanglement can be coherently understood in our unified framework. Our fluctuation theorem can be applied to a wide range of physical systems and dynamics to query the reversibility of a quantum state for the given quantum processing channel involving coherence and entanglement.
We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes' principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.