Correlations, operations and the second law of thermodynamics

Abstract

Completely positive trace preserving maps are essential for the formulation of the second law of thermodynamics. The dynamics of quantum systems, correlated with their environments, are in general not described by such maps. We explore how this issue can be fixed by describing the classical analogue of this problem. We consider correlated probability distributions, whose subsequent system dynamics is ill-described by stochastic maps, and prescribe the correct way to describe the dynamics. We use this prescription to discuss the classical version of the second law, valid for correlated probability distributions.

References in corpus (10)

• The second laws of quantum thermodynamics
• A nano heat engine beyond the Carnot limit
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Single ion heat engine with maximum efficiency at maximum power
• Thermodynamical Control by Frequent Quantum Measurements
• Extracting work from a single heat bath through feedback
• Characterizing quantum dynamics with initial system-environment correlations
• A quantum violation of the second law?
• Thermodynamics of quantum coherence
• Entropy bounds for quantum processes with initial correlations

Cited by in corpus (4)

• Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping
• Quadratic Enhancement in the Reliability of Collective Quantum Engines
• Preparations and Weak Quantum Control can Witness non-Markovianity
• Quantum work fluctuations versus macrorealism in terms of non-extensive entropies