Quantum mean-square predictors and thermodynamics

Abstract

Thermodynamic quantities, such as heat and work, are not functions of state, but rather of the process undergone by a physical system. Assessing them can therefore be difficult, since it requires probing the system at least twice. This is even more so when these quantities are to be assessed at the stochastic level. In this letter we show how to obtain optimal estimates of thermodynamic quantities solely from indirect measurement unravellings of an auxiliary system. The method always yields the true average. And the mean-squared error of the prediction is directly proportional to how well the method estimates the variance. As an application, we study energy fluctuations in a driven system, and in an avoided crossing work protocol.

References in corpus (9)

• Thermodynamic uncertainty relation for biomolecular processes
• Fluctuation theorems: Work is not an observable
• The unlikely Carnot efficiency
• Non-equilibrium quantum fluctuations of work
• Fluctuation theorems in driven open quantum systems
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Probing Quantum Interference Effects in the Work Distribution
• Measurement-dependent corrections to work distributions arising from quantum coherences
• Comparison between quantum jumps and master equation in the presence of a finite environment

Cited by in corpus (5)

• Work extraction from unknown quantum sources
• Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
• Energy conservation and fluctuation theorem are incompatible for quantum work
• Quantum work: Reconciling quantum mechanics and thermodynamics
• Fluctuation theorems for genuine quantum mechanical regimes