The Demon of Interrelation

Maxwell’s Demon and Thermodynamics

For the purposes of this treatment there are several quantities that need to be clearly defined, namely energy, work, entropy, and information. Energy refers to the capacity of a system to do work, which is itself the transfer of energy that occurs when a force moves an object, and colloquially refers to the ability “to do things”; $W=\int \vec{F}\cdot d\vec{r}$, where $W$ is work, $\vec{F}$ is force, and $d\vec{r}$ is displacement. Entropy is, on a macroscale, the outcome of spontaneous changes in the system; while on a microscale entropy is an evaluation of the probability of being in a state given an ensemble of microstates; $S=k_B\ln \Omega$, where $S$ is entropy, $kB$ is Boltzmann’s constant, and $\Omega$ is the number of microstates. Information is a way to quantify the amount of surprise that might be had given a particular outcome of some random variable, with Shannon entropy being the expected value of information of a random variable; $H(X)=-{\sum }_{i}p(x_i){\log }_{2}p(x_i)$, where $H(X)$ is Shannon entropy, $p(x_i)$ is the probability of outcome $x_i$.

Maxwell’s demon is a creature that sits on the boundary of two boxes filled with particles, the job of this demon is to lift up a gate when a high energy particle would hit the left hand side of the gate or when a low energy particle would hit the right hand side of the gate. The result of the demon’s work is the sorting of two average energy boxes into a high and low energy box, thus allowing someone to do work with the energy differential created. The problem is that this apparently violates the second law of thermodynamics, which is essentially that “entropy is always increasing” or equivalently “heat always flows spontaneously from hotter to colder regions of matter”; $\Delta S\ge 0$, where $\Delta S$ is the change in entropy of an isolated system. When one considers the demon themself in the calculation the violation disappears, as the entropy cost from information erasure, via Landauer’s principle, offsets the entropy decrease via particle separation.; $\Delta S_{erasure}\ge \frac{k_B\ln (2)}{bit}$, where $\Delta S_{erasure}$ is the minimum entropy increase associated with erasing one bit of information.

This points to an interesting feature of physics, the idea that one can use information as a method of extracting work from systems. The Szilard engine does this by making a Maxwell’s demon with a single particle, a shutter, and a pair of pistons, wherein a shutter is closed when a particle is on one side allowing for the pressure difference to perform work; $W_{max}=k_{B}T\ln (2)$, where $W_{max}$ is the maximum work extractable from a Szilard engine, $T$ is temperature. Landauer’s principle allows generalisation such that, any information with a physical representation is embedded in the statistical mechanical degrees of freedom of a physical system. While designed to provide a lower bound on the amount of energy for computation, conceptually it points at how information is physically embedded in the systems they exist within and vice versa; $E_{min}=k_{B}T\ln (2)$, where $E_{min}$ is the minimum energy required to erase one bit of information at temperature $T$.

These changes can occur on both macro-scale and micro-scale processes, with the seeming ability to extract work from non-equilibrium systems. The Jarzynski equality shows that fluctuations in work still obey specific constraints — these are distinct from the constraints that govern the average free energy of a system; $⟨e^{-\beta W}⟩=e^{-\beta \Delta F}$, where $\beta =\frac{1}{k_{B}T}$, $W$ is work, $\Delta F$ is the free energy difference, and $⟨⟩$ denotes an average over all possible realizations. Specifically the importance of microstates are brought up insomuch that a singular realisation of a microscopic system in an equilibrium state can locally “violate” the second law, but will comply statistically, and when integrated produce the equilibrium value. So, when one attempts to extract work out of a microscopic system you are either borrowing from the full realisation of the system via noise, which will later average out, or leveraging information at a thermodynamic cost in order to change the system; $\Delta S_{total}=\Delta S_{system}+\Delta S_{information}\ge 0$, where $\Delta S_{total}$ is the total entropy change, $\Delta S_{system}$ is the entropy change of the physical system, and $\Delta S_{information}$ is the entropy change associated with information processing.

The Plane of Interrelation

For the purposes of this treatment there are several concepts that need to be clearly defined, namely interrelations, boundaries, obligations, and relationships. The plane of interrelation is a metaphysical space where psychological constructs can exchange information. Boundaries are configurational spaces where defined interactions produce obligations between entities, while obligations are a force applied to an entity by a social or psychological mechanism when a boundary is interacted with. Relationships are phases formed from boundaries and obligations that keep two entities in a specific configuration.

The plane of interrelation is place where connections are made, where a parent finds love with a child and where a child finds fear for a particular twig. Entities have psychological “states” akin to energy states in physical systems, for most interactions the perceived energy state of an interlocutor is more important than the actual one. The plane operates based on the exchange of information through words, gestures, and various social games. Importantly the plane of interrelation is governed by patterns that emerge from repeated interactions.

The primary drivers of patterns are boundaries and obligations, which act as the partition function of Maxwell and work respectively. Boundaries are used to regulate the flow of information and influence between entities, such as explicitly asking not to call after 9 PM or implicit like maintaining physical distance from strangers. Obligations represent the psychological forces that compel action, when someone does you a favor you feel obligated to help, when you violate a boundary you feel obligated to redress them. These boundaries and obligations are either applied directly interpersonally, like a particle-particle, or via social norms and laws, like a field.

Relationships are similar to a form of phase transition, where a set of boundaries and obligations balance in just the right way to sequester entities in similar spaces or within specific configurations with regards to one another. By using boundaries one can set distances that minimize the surprise different entities may feel during their interactions, while obligations allow entities to fine-tune boundaries. This balance is similar to a Szilard engine, in that information on their nature allows one to extract meaningful work, such as in networking. Relationships are stabilised via personal (micro) or social (macro) boundaries and obligations, the difference between a friendship and a fellow citizen.

The Demon of Interrelation

For the purposes of this treatment there are several concepts that need to be clearly defined, namely the demon of interrelation, manipulation, and distortion. Just like Maxwell’s demon, the demon of interrelation attempts to extract work from others via the leveraging of information. Manipulation of boundaries is how a demon uses deliberately ambiguous boundaries to harvest obligation. Reality distortion is where a demon takes control of a narrative and modifies how relationships are perceived.

The demon’s goal is to create some benefit from themselves (negentropy) at the expense of others (entropy) by controlling information about the system they are manipulating. These demons are often called narcissists, psychopaths, and sociopaths, because there requires some inherent disregard for “fair play” in order to be a demon. The demon feeds on the energy of others through emotional labor, cognitive effort, and attention which can be translated to meaningful currency in a modern economy. The consequences of this behaviour is an asymmetric aggregation of power and social favours towards the demon and, according to Landauer’s principle, a slow withering of the social system they are manipulated.

Manipulation is one of the more classic methods of a demon, and lines up well with how Maxwell’s demon operates. By maintaining an inconsistently applied boundary the demon is able to capture energy, in the form of obligations, from others through the information they have about a relationship. So a demon might take the phrase “Can you help me move this weekend?” and claim they only agreed to “stop by briefly” if the demon find something else the demon want to do, while insisting you promised “a full weekend of assistance” when they need help with their own move. On a macro-scale this behaviour is seen in organisations where policies (boundaries) remain strategically ambiguous, giving them freedom to enforce them strictly or flexibly and creating a system where obligations flow towards those that control the narrative.

Reality distortion is the most powerful tool in the demon’s toolbox, it has to do with the ability to control how entities experience boundaries and obligations. By modifying the “experienced” reality of an entity a demon is capable of creating local perturbations and extract obligations from others via asymmetric information. Classic methods include gaslighting (“That never happened”) and reframing of motives (“I was just trying to help”), allowing the demon to steer a relationship such that absurd boundaries are accepted and reasonable boundaries. There is a feedback loop where the more people that believe a distortion the harder it is to remove it such as in cults, but conversely the energy cost of erasing contradicting information from the outside world increases according to Landauer’s principle.

The Demon’s Scales

For the purpose of this treatment there are several concepts that need to be clearly defined, namely relationship fluctuations, information equilibrium, obligation balance, and systemic resilience. Relationship fluctuations are the natural variations in boundaries and obligations that occur in a relationship. In a system of entities, information equilibrium is the balance of knowledge while obligation balance is the distribution of social debts. Systemic resilience describes the ability of a system to maintain global stability despite local perturbations.

A normal relationship is not static as they are globally non-equilibrium, such as a parent-child relationship evolving, or have local fluctuations, a natural mechanism for a social Szilard engine to be set upon. However, the overall patterns of relationships conform to predictable constraints when averaged over a specific spatiotemporal environment for the entities, as is required by Landauer’s princple. Local violations of boundaries and accruement of obligations occur, but in a healthy relationship the obligations will tend towards balance either at zero (low-stakes), infinity (unconditional), or some middle point (friendship). In society-wide situations this appears as extremes of either a low or high social trust, and both have different mechanisms for evening out such as vigilantism (low trust) and legal action (high trust).

Key to the accruement of obligations is the ability to exchange information, and in a relationship the exchange of information has an associated cost. One cannot expect someone to feel an obligation for a slight that was never brought to the light, but the process of communicating that slight and why an obligation is warranted has a cost. In this a demon is capable of distorting reality and make the cost of communicating higher, such as excessively complex system for filing complaints. A society may have local points of disequilibrium but should tend towards information and obligation balancing, similar to levels of taxation and the right to know what taxes are being spent on.

Systemic resilience of system of relationships is how one is capable of form a stable relationship, which on a macroscale is a prerequisite for social cohesion. There are two possible failure modes, if a relationship is too resilient than a demon can continually harvest small amounts of obligations and if the relationship is not resilient enough then entities will not tolerate realistic failures. Resilience is maintained by either modulating the obligation force a boundary exerts on an entity or by arranging relationships so they are interlocking. Similar to the Jarzynski equalities statistical averaging, the structure of macro-scale relationships limit local fluctuations in obligation.