Philippe Faist, Frédéric Dupuis, Jonathan Oppenheim, Renato Renner
Landauer's Principle states that the work cost of erasure of one bit of information has a fundamental lower bound of kT ln(2). Here we prove a quantitative Landauer's principle for arbitrary processes, providing a general lower bound on their work cost. This bound is given by the minimum amount of (information theoretical) entropy that has to be dumped into the environment, as measured by the conditional max-entropy. The bound is tight up to a logarithmic term in the failure probability. Our result shows that the minimum amount of work required to carry out a given process depends on how much correlation we wish to retain between the input and the output systems, and that this dependence disappears only if we average the cost over many independent copies of the input state. Our proof is valid in a general framework that specifies the set of possible physical operations compatible with the second law of thermodynamics. We employ the technical toolbox of matrix majorization, which we extend and generalize to a new kind of majorization, called lambda-majorization. This allows us to formulate the problem as a semidefinite program and provide an optimal solution.
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http://arxiv.org/abs/1211.1037
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