In 1961 Rolf Landauer linked information and thermodynamic entropy by showing that erasing or combining bits of memory must be accompanied by an increase in entropy. For the first time since then, a team of physicists have experimentally verified this principle.

According to Landauer’s principle, any logically irreversible transformation of information results in, at best, some small dissipation of heat. The specific amount depends on the operating temperature—per bit, it amounts to around 3×10-21 joules at room temperature. This energy is the Landauer limit, and controls the maximum energy efficiency of computers (it's similar to the Carnot efficiency in heat engines, both of which are related to entropy).

Measuring such a tiny amount of energy in a memory storage devices is, to say the least, challenging. But now, a team from École Normale Supérieure, the University of Kaiserslautern, and the University of Augsburg has managed to do so.

Logically irreversible This term refers to an action where the input can't be uniquely determined from the output. For example, any binary Boolean operation (AND, OR, NAND, XOR) falls in this category. Erasing information is also logically irreversible. In both cases, some information is being "destroyed"—you can't reverse the procedure to get the starting information back. More technically, during a logically irreversible operation the number of possible logical states of a computation are decreased (for instance, two bits might be reduced to one in a Boolean operation or a single bit might be erased). In order to avoid violating the second law of thermodynamics (and to obey Landauer's principle), this must result in an increase in entropy through heat dissipation, increasing the number of possible physical states to balance the decrease in possible logical states.

Currently, our computers operate around a thousand times the Landauer limit. But as computer speeds increase, we need to move closer to this maximum efficiency to control power consumption and heat dissipation. However, until now, Landauer’s principle hasn’t been experimentally verified.

Their experimental approach is similar to one we previously covered being used to run a microscopic heat engine. The authors here represented one bit of memory with a single two-micrometer silica bead held in water between glass slides. They used a laser to create a double potential well by rapidly switching the focus of the laser between two positions. This functioned as an optical tweezer, holding the bead in one of the positions. The left position represented the 0 state, and the right the 1 state.

In this system, erasing the memory is moving the bead to the right-hand well regardless of the initial position (0 to 1, or 1 to 1). The team managed this by first lowering the energy barrier between the two potential wells, then tilting the glass slide. This tilt created a viscous force that moved the bead to the right.

Now, let’s consider this operation in terms of entropy. Initially, the bead could be in either well, so the probability of each is one-half. This corresponds with a small but known entropy. After the erasure, the entropy is zero since the final position is known. Therefore, to satisfy that pesky second law of thermodynamics, the procedure must transfer (at minimum) the initial entropy in the surrounding environment.

This entropy increase manifests as heat dissipated in the surrounding water during the erasure. The actual entropy produced depends on the timing of the erase cycle. The researchers found that shorter cycles (meaning faster movement) dissipated more heat. As the cycle time gets larger and larger, the entropy asymptotically decreases to the Landauer limit.

This behavior makes sense: in macro thermodynamic systems, no process (like heat addition or piston work) is actually reversible; every real process generates some amount of entropy. We can approximate processes as reversible, though, if they move slow enough compared to the system response. Here, in a microscopic single-particle system, the researchers found a similar time-dependent behavior. Fundamentally, though, a minimal amount of entropy must be produced in a logically irreversible process—the Landauer limit—and this study finally confirmed this principle.

Nature, 2012. DOI: 10.1038/nature10872 (About DOIs)