commit a289c8d5d5468739575b34067ca83639a33965a4
parent ca8c689f7baf43b710ffe45e96c65ab813658add
Author: orx <orx@web>
Date: Tue Nov 15 14:53:42 +0100
Added Landauer limit according to Wim
Diffstat:1 file changed, 10 insertions(+), 0 deletions(-)
diff --git a/information_and_energy.mdwn b/information_and_energy.mdwn
@@ -1,5 +1,7 @@
Related to: Thermodynamics
+###Information and entropy relation to energy
+
We can distinguish 2 types of information in relation to abstract and physical worlds:
- Unbound information - possible symbols or states are understood as purely abstract and not related to any physical system. That is information used in mathematics.
@@ -22,3 +24,11 @@ The thermodynamic system can be one of the next 3 types:
First two are only abstract or temporary states of the systems. We even cannot get any information about state of the isolated system. All computational systems are open, as computational devices are material, and material is being mined, formed, assembled, disassembled, so any computation, no matter how abstract and symbolic, is bound to the material and energy exchange.
When the abstract mathematical or symbolic processing is done in pure mind of the human, there is an energy and material exchange needed by related biological processes in the brain.
+
+###Energy needed for signal modulation
+
+Landauer's principle asserts that there is a minimum possible amount of energy required to erase one bit of information, known as the Landauer limit: E=k_B T ln 2 (k_B is the Boltzmann constant and T is the temperature). For T equal to room temperature 20 °C, we can get the Landauer limit of 0.0175 eV (2.805 zJ) per bit erased.
+
+The equation can be deduced from the Boltzmann's entropy formula S=k_B ln W , considering that W is the number of states of the system, which in case of a bit is 2, and the entropy S is defined as E/T. So the operation of erasing a single bit increases the entropy of a value of at least k_B ln 2}, emitting in the environment a quantity of energy equal or greater than Landauer limit.
+
+It puts a fundamental ceiling on the increase in the number of computations per joule of energy dissipated. Until recently, this increase has been exponential (doubling every 2 years), so by 2048 we would reach Landauer's limit. Probably the slowdown already increased the doubling to 2.6 years, which means there will be more limited increases in performance per Watt.
