Relativistic motion through a thermal bath as a thermodynamic resource

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.

Figures (3)

• Figure 1: (Color Online) Affinity $\mathcal{A}$ (a) and current $-\mathcal{J}$ (b) of three level system, as function of inverse temperature $\beta$ for three different value of velocity small $u=0.2$ (black dot-dashed), intermediate $u=0.6$ (blue dashed) and ultrarelativistic $u=0.99$ (red solid). Other parameter values are $\omega_{10}=1.0, \omega_{21}=3.1$.
• Figure 2: (Color Online) Relative uncertainty $\delta^2$ (a) and product of relative uncertainty with entropy production $\mathcal{\delta}^2\Sigma$ (b) as a function of inverse temperature $\beta$ for different values of velocity $u$. Other parameter values are same as Fig. \ref{['fig:fig1']}.
• Figure 3: (Color Online) Plot of maximum extractable work $\mathcal{W}_\mathrm{max}$ of steady-state $\hat{\rho}^\mathrm{ss}$ for different values of velocity $u$. Other parameter values are same as Fig. \ref{['fig:fig1']}