Information is often considered as an abstract entity, but it is always stored and processed by a physical medium. As such, it obeys all the restrictions and possibilities related to the laws of physics. In 1961, Rolf Landauer proposed the existence of a fundamental energetic cost associated with information processing: each time information is processed in a logically irreversible way, at least kTln2 of heat is released, on average, into the surrounding bath. This principle also resolves the long-standing threat to the second law of thermodynamics posed by Maxwell's demon. Although the Landauer principle has been widely accepted, it remained untested and controversial for more than half a century. The small amount of heat released as a result of logically irreversible operations was hard to detect in any conventional information-processing device. With recent technical and theoretical advances in micromanipulations, this became possible. In my graduate study, I used and calibrated a feedback trap to execute logical operations and measure the tiny energetic cost associated with them. I start this thesis with a brief review of stochastic thermodynamics and information theory, followed by my experimental approach. I present two feedback traps: one that I inherited and the other that I developed later in my studies. Both traps use the same real-time calibration method based on a recursive maximum likelihood algorithm. The calibrated trap was initially used to test the Landauer principle and show that erasing a symmetric one-bit memory requires kTln2 work on average, while no work is required for similar protocols with no net erasure. This experiment confirmed Landauer's hypothesis that information is physical. In my later work, I explored information in more complex environments. I experimentally studied erasure for a memory encoded in an asymmetric double-well potential. I found that the average work to erase can be below kTln2, as predicted by a recent theory. Surprisingly, erasure protocols that differ subtly give measurably different values for the asymptotic work, a result I explain by showing that one protocol is symmetric with respect to time reversal, while the other is not. The differences between the protocols help clarify the distinctions between thermodynamic and logical reversibility. I further explored the same phenomena divorced from Landauer's principle, where a system starts and ends in the same equilibrium state, and I show that arbitrarily slow transformations, produced by smooth deformations of a double-well potential, need not be reversible. Finally, I present my work towards a direct test of the form of the Shannon entropy function.
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Thesis advisor: Bechhoefer, John
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