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arXiv:2512.07567

Relativistic motion through a thermal bath as a thermodynamic resource

Rahul Shastri

quant-phhep-thSubmitted Dec 8, 2025• Announced Dec 9, 2025• 0 citations• Revised Dec 20, 2025 (v2)
v1 · Dec 8, 2025v2 · Dec 20, 2025
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Abstract

We show that a localized quantum system following an arbitrary stationary trajectory and weakly interacting with a stationary thermal bath of a massless scalar field is generically driven into a non-Gibbs steady state by relative motion alone, even without external driving or multiple baths. Relative motion between the system and the bath modifies the standard Kubo-Martin-Schwinger (KMS) relation, preventing relaxation to a Gibbs state. The resulting steady states fall into two distinct classes: (i) nonequilibrium steady states (NESS) with persistent probability currents, and (ii) current-free non-Gibbs steady states characterized by a frequency-dependent effective inverse temperature. We then focus on the simplest stationary trajectory, namely uniform relativistic motion with respect to a thermal bath. Using a three-level system as an illustrative example, we demonstrate that the former class can function as noisy stochastic clocks, while the latter possesses finite nonequilibrium free energy, enabling work extraction or storage, highlighting their potential as quantum batteries.

Comments
6 pages, 3 figures, Comments are welcome!

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We show that a localized quantum system following an arbitrary stationary trajectory and weakly interacting with a stationary thermal bath of a massless scalar field is generically driven into a non-Gibbs steady state by relative motion alone, even without external driving or multiple baths. Relative motion between the system and the bath modifies the standard Kubo-Martin-Schwinger (KMS) relation, preventing relaxation to a Gibbs state. The resulting steady states fall into two distinct classes: (i) nonequilibrium steady states (NESS) with persistent probability currents, and (ii) current-free non-Gibbs steady states characterized by a frequency-dependent effective inverse temperature. We then focus on the simplest stationary trajectory, namely uniform relativistic motion with respect to a thermal bath. Using a three-level system as an illustrative example, we demonstrate that the former class can function as noisy stochastic clocks, while the latter possesses finite nonequilibrium free energy, enabling work extraction or storage, highlighting their potential as quantum batteries.
We investigate when temporal ordering becomes operationally meaningful in relativistic quantum field theory using localized detector models. A time parameter alone does not ensure that different sequences of operations are physically distinguishable. We show that distinguishability arises when the state satisfies the Kubo--Martin--Schwinger (KMS) condition and the detector couples through non-commuting observables. We consider uniformly accelerated two-level detectors interacting with a quantum field in the Minkowski vacuum. The restriction of the vacuum to the detector trajectory induces a thermal response characterized by the Unruh temperature and the Tolman profile. For sequential couplings through distinct observables, the reduced detector state depends on the ordering of interactions already at second order, with a dependence controlled by the KMS parameter. This asymmetry is quantified using quantum relative entropy. In a minimal model, the relevant states form a family of non-commuting Gibbs states with identical spectra and different generators, yielding a closed-form expression depending only on the dimensionless combination of temperature and detector energy scale.
Collision models provide a simple and versatile setting to capture the dynamics of open quantum systems. The standard approach to thermalization in this setting involves an environment of independent and identically prepared thermal qubits, interacting sequentially for a finite duration Δ t with the system. We compare this to a two-bath scenario in which collisional qubits are prepared in either their ground or excited states and the environment temperature is encoded in system-environment couplings. The system reaches the same thermal steady state for both settings, although even in this limit they describe fundamentally different physical processes, with the two-bath setup yielding a nonequilibrium state with finite heat currents. Non-Markovian dynamics arises when intraenvironment interactions in either setting are introduced. Here the system in the single-bath setup again reaches a steady state at the canonical temperature of the bath, but the nonequilibrium steady state of the two-bath setup tends to a different temperature due to the generation of strong system-environment and intraenvironment correlations. The two-bath setting is particularly suited to studying quantum trajectories, which are well defined also for the non-Markovian case. We showcase this with a trajectory analysis of the heat currents within a two-point measurement scheme. Finally, we consider how our results are impacted when the system-environment interaction leads to strict homogenization. Our results provide insights into the dynamics and thermodynamics of thermalization towards nonequilibrium steady states and the role of non-Markovian interactions.
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The Redfield quantum master equation is widely used to study the dynamics of interacting sub-systems that are weakly coupled to baths. Redfield dynamics under secular approximation preserves positivity of the reduced density operator and thermalizes the system into a Gibbs state at equilibrium. Long-time effects arising from non-secular terms are often neglected, but depending on the system spectrum and relative bath couplings, non-secular contributions are shown here to drive the system into a non-Gibbs state. For two strongly interacting quantum oscillators with independent baths at equal temperature, we analyze the microscopic origin of the deviations from Gibbs statistics. Provided that the oscillators are unequally damped by their baths, we show that steady state occupation numbers can significantly deviate from a Boltzmann distribution due to an excitation flux driven by bath-induced coherences between nearly-degenerate oscillator levels. Conditions for the recovery of thermal Gibbs statistics are discussed and experimental signatures suggested.
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