Discrete fluctuations in memory erasure without energy cost

Abstract

According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs, the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with the discrete variable. Here we study the {\it discrete} fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.

References in corpus (10)

• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Thermodynamics of quantum systems with multiple conserved quantities
• An all-optical nanomechanical heat engine
• Stochastic thermodynamics with information reservoirs
• Erasure without work in an asymmetric, double-well potential
• Information erasure without an energy cost
• The Second Laws for an Information driven Current through a Spin Valve
• Conservation laws and symmetries in stochastic thermodynamics
• Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles
• Thermodynamic cost of reversible computing

Cited by in corpus (14)

• Hybrid Thermal Machines: Generalized Thermodynamic Resources for Multitasking
• Noncommuting conserved charges in quantum thermodynamics and beyond
• Non-Abelian Quantum Transport and Thermosqueezing Effects
• Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond i.i.d. scaling
• Quantum heat engine operating between thermal and spin reservoirs
• Nonequilibrium Thermodynamics of Restricted Boltzmann Machines
• Work Extraction and Landauer's Principle in a Quantum Spin Hall Device
• Quantum thermodynamics with multiple conserved quantities
• Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes
• Thermodynamics of memory erasure via a spin reservoir
• Information Erasure
• Memory erasure with finite-sized spin reservoir
• Universal Statistics of Charges Exchanges in Non-Abelian Quantum Transport
• Quantum thermodynamics under continuous monitoring: a general framework