Jarzynski Equality for Driven Quantum Field Theories

Abstract

The fluctuation theorems, and in particular, the Jarzynski equality, are the most important pillars of modern non-equilibrium statistical mechanics. We extend the quantum Jarzynski equality together with the Two-Time Measurement Formalism to their ultimate range of validity -- to quantum field theories. To this end, we focus on a time-dependent version of scalar phi-four. We find closed form expressions for the resulting work distribution function, and we find that they are proper physical observables of the quantum field theory. Also, we show explicitly that the Jarzynski equality and Crooks fluctuation theorems hold at one-loop order independent of the renormalization scale. As a numerical case study, we compute the work distributions for an infinitely smooth protocol in the ultra-relativistic regime. In this case, it is found that work done through processes with pair creation is the dominant contribution.

19 pages, 6 figures

References in corpus (13)

• Fluctuation theorems: Work is not an observable
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Non-equilibrium quantum fluctuations of work
• Fluctuation theorems in driven open quantum systems
• The Wigner Entropy Production Rate
• Holevo's bound from a general quantum fluctuation theorem
• Microcanonical quantum fluctuation theorems
• Assessing the non-equilibrium thermodynamics in a quenched quantum many-body system via single projective measurements
• Jarzynski equality in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Moments of work in the two-point measurement protocol for a driven open quantum system
• Understanding quantum work in a quantum many-body system
• Another proof of Gell-Mann and Low's theorem

Cited by in corpus (23)

• Fluctuation Theorems for a Quantum Channel
• Work as an external quantum observable and an operational quantum work fluctuation theorem
• Quantum Martingale Theory and Entropy Production
• Work distributions on quantum fields
• Quantum Fluctuation Theorems
• Stochastic thermodynamics of relativistic Brownian motion
• Information loss in effective field theory: entanglement and thermal entropies
• Quantum coherence and criticality in irreversible work
• Quantum work distributions associated with the dynamical Casimir effect
• Thermodynamic uncertainty relation for quantum first passage process
• The First Law of Quantum Field Thermodynamics
• Nonequilibrium Green's function's approach to the calculation of work statistics
• Strong coupling from non-equilibrium Monte Carlo simulations
• Exchange fluctuation theorems for strongly interacting quantum pumps
• Universal Quantum Fluctuation-Dissipation Relation for Systems Far From Equilibrium
• Path integral approach to the calculation of the characteristic function of work
• Promoting Fluctuation Theorems into Covariant Forms
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• Operational work fluctuation theorem for open quantum systems
• Modified Jarzynski equality in a microcanonical ensemble
• Entropy production due to spacetime fluctuations
• Thermodynamic uncertainty relations for relativistic quantum thermal machines
• Relativistic entropy production for quantum field in cavity