Thermodynamic cost of acquiring information
  Connections between information theory and thermodynamics have proven to be very useful to establish bounding limits for physical processes. Ideas such as Landauer's erasure principle and information assisted work extraction have greatly contributed not only to enlarge our understanding about the fundamental limits imposed by nature, but also to enlighten the path for practical implementations of information processing devices. The intricate information-thermodynamics relation also entails a fundamental limit on parameter estimation, establishing a thermodynamic cost for information acquisition. More specifically, we show that the amount of information that can be encoded in a physical system (and consequently extracted) by means of any process is limited by the dissipated work during the implementation of the process. This includes a thermodynamic trade-off for information acquisition. Likewise, any information acquisition process is ultimately limited by the second law of thermodynamics. Such a trade-off may find applications in several areas of knowledge, since parameter estimation lies in the building basis of all natural sciences and several technological applications, such as metrology. 
Kaonan Micadei, Roberto M. Serra and Lucas C. Celeri
quant-ph cond-mat.stat-mech