Compatibility of linear-response theory with the Second Law of Thermodynamics and the emergence of negative entropy production rates

Abstract

The reliability of physical theories depends on whether they agree with well established physical laws. In this work, we address the compatibility of the Hamiltonian formulation of linear-response theory with the Second Law of Thermodynamics. In order to do so, we verify three complementary aspects often understood as statements of the Second Law: 1. No dissipation for quasistatic process; 2. Dissipation for finite-time processes; 3. Positive entropy production rate. Our analysis focus on two classes of nonequilibrium isothermal processes: slowly-varying and finite-time but weak ones. For the former, we show that these aspects are easily verified. For the later, we present conditions for the achievement of the first two aspects. We also show that the third one is not always verified, presenting an example based on Brownian motion in which we observe negative values in the entropy production rate. In particular, we compare linear-response and exact results for this example.

arXiv comment11 pages, 7 figures

References in corpus (21)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Non-Markovian dynamics in open quantum systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Optimal finite-time processes in stochastic thermodynamics
• Thermodynamic metrics and optimal paths
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• Non-Markovianity and negative entropy production rates
• Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate
• Optimal driving of isothermal processes close to equilibrium
• Thermodynamic meaning and power of non-Markovianity
• Entropy production and correlations in a controlled non-Markovian setting
• Minimal dissipation in processes far from equilibrium
• From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic Behavior: An Overview
• Degenerate optimal paths in thermally isolated systems
• Thermodynamic utility of Non-Markovianity from the perspective of resource interconversion
• Fourier-positivity constraints on QCD dipole models
• On the positivity of Fourier transforms

Cited by in corpus (22)

• Thermodynamic control -- an old paradigm with new applications
• Negative entropy production rates in Drude-Sommerfeld metals
• Heat current and entropy production rate in local non-Markovian quantum dynamics of global Markovian evolution
• Generalised linear response theory for the full quantum work statistics
• Adiabatic processes like isothermal processes
• Analytical solution for optimal protocols of weak drivings
• Fluctuation theorem for irreversible entropy production in electrical conduction
• Optimal work fluctuations for finite-time and weak processes
• Multiparty Spohn's theorem for a combination of local Markovian and non-Markovian quantum dynamics
• Quantum Ising chain with time-averaged work in linear response theory
• Global optimization and monotonicity in entropy production of weak drivings
• Nano-welding of quantum spin-$1/2$ chains at minimal dissipation
• Full Quantum Work Statistics for Non-Homogeneous Many-Body Systems
• Fluctuation theorem for time-averaged work
• Analytical shortcuts to adiabaticity of weakly driven processes
• Casimir-Onsager matrix for weakly driven processes
• Thermodynamic optimization equalities in weakly driven processes
• Optimal finite-time processes in weakly driven overdamped Brownian motion
• Kibble-Zurek scaling from linear response theory
• Minimal dissipation with viscoelastic baths in weakly driven processes
• Quantum refrigerator embedded in spin-star environments: Scalings of temperature and refrigeration time
• Unifying Kibble-Zurek Mechanism in Weakly Driven Processes