This project will investigate four possible means of avoiding the second law of thermodynamics:

  1. Room Temperature thermionic devices
  2. Bipolar membrane devices
  3. High Temperature thermionic devices
  4. Magnetic devices utilizing attractors in nonlinear phase space and/or the concept of "second sound"

We will also discuss mesoscopic devices like the Graphene Energy Harvester and an analogous system using a superparamagnetic particle and a micron-scale pickup coil, but they requre integrated circuit etching technology, so we will not be replicating them here. Some hackers have built IC etching equipment in their home labs and we encourage them to try these.

Note I say avoiding, not violating, the second law: this is done in a manner analogous to how complex numbers have different properties than real numbers: when you start with a different set of axioms, you arrive at different maths.

In mathematical physics, we try to build models with minimal sets of assumptions. This is because, historically speaking, assumptions and constants have typically been indications of some incomplete understanding of the underlying physics we are attempting to model. The way it is taught today, an introductory student of Thermodynamics could be forgiven for thinking that the laws of thermodynamics are a set of such assumptions, but the second law in particular is based on a set of more fundamental mathematical assumptions, which are in question here.

 Firstly, the second law has an implicit assumption that all states in an ensemble have roughly the same order of magnitude of probability of receiving energy from another state in the ensemble during a small time interval. This assumption is called ergodicity, and if a statistical ensemble is ergodic, energy concentrated in one state will always spread out until the system reaches a steady state, where entropy is maximized. This is why, with the second law, we say entropy tends to increase, or heat flows from hot to cold. Ensembles in thermodynamics have roughly the same mathematical structure as Markov chains, so to put this another way, in order to get the second law of thermodynamics, we have to assume that it is impossible to build an ensemble that behaves like an absorbing (or oscillating) Markov chain.

In standard statistical mechanics there is also the assumption of "weak coupling" undergirding the second law. Weakly coupled quantum systems will tend not to display any correlations between interacting particles or quanta of energy, and such systems lead naturally to ergodicity. But in biology it is known that various enzymes and receptors are specifically not weakly coupled, and in condensed matter physics, the study of "correlated electron matter", where weak coupling should not be assumed, is a sizeable and active field. So if we know of counterexamples here, why not look for counterexamples to ergodicity?

Such a counterexample in and of itself isn't particularly interesting, but let's imagine an ensemble where the absorbing state happens to be a capacitor, or other energy storage system which we know how to harness. Then that capacitor can be periodically tapped for energy, dissipated during work into a second system. If that second system is in thermal contact with the first system, then the energy will eventually get captured again in the absorbing state, where it can be tapped again. Assuming the energy to switch the capacitor behavior is stored upon each discharge in one of the two systems involved, then the combination of the two systems has been engineered to minimize the poincare recurrence time in a predictable and useful way. When one views the systems separately, it appears that work is made available periodically, but when one views these as a single system, I propose we define a new quantity, called "play". If ergodicity is violable, many other interesting possibilities arise

These days, there are an increasing number of apparent counterexamples to the assumption of ergodicity, like the Graphene Energy Harvesters at the University of Arkansas, and Epicatalytic thermal "diodes" at UC San Diego.

More references : 1 2 3 4 5 6 7 8

When we don't make the assumption of ergodicity, then we must construct definitions our new thermodynamic variables without them. Existing thermodynamics is still self consistent, but its variables and equations cannot be used to falsify a superset of itself, because those variables cannot apply if the assumptions used to define them don't apply.

From the current set of experiments, these "Maxwell's Zombie" systems seem to have a few features in common: they often involve phase changes, absorbing Markov dynamics, modulation of boundary conditions/varying the boundary of the ensemble, and "biasing potential energy", which is often not used up in the operation of the device, but rather biases the flow of other energy to be harvested. These systems usually involve a process, measurable in terms of electron volts or temperature, which defines the minimum operating temperature of the device as a "virtual" heatsink.. Dan Sheehan's recent research discusses a number of other common features of these systems as well.

For the case of the Graphene Energy Harvester, an electrostatic charge is placed on the graphene sheet, which vibrates from thermal motion with millivolt energies sufficient to overcome the forward voltages of MIM diodes in a full bridge rectifier. The excess energy harvested from thermal motion becomes trapped in a capacitor, which may be considered the "absorbing state" of the system. But because we know how to use capacitors, we can simply periodically close the switch and use the resulting energy, like water in a hydroelectric reservoir. This process changes the absorbing Markov Chain ensemble from a closed system to an open system.

Another example is the self-charging thermionic capacitor: This time, the biasing energy is the single heat bath the capacitor is immersed in, and the operating temperature is defined in eV by the work functions of the two metal plates involved. If the operating temperature is high enough, the low work function material will emit more electrons than the high work function material, developing a net charge between the plates which may be harvested. Note that unlike a Carnot engine, this device requires no heat sink, the "virtual heat sink" is defined only by the work functions of the two metals. Similar to the Graphene Energy Harvester, the charge on the capacitor may be tapped to do work in an external system.

Most of these devices require extreme operating conditions or semiconductor fabrication capabilities, and so are not accessible to us mere mortals. During the course of this project, we will attempt to construct some devices which are approachable and buildable by the Hackaday community, as well as document the fundamental physics and math involved.