Panpsychism and Landauer's Principle: A Theoretical Framework for Consciousness Measurement
A being with organically coordinated processes that involve the knowledge of the self or in a much broader sense the knowledge of its own conscious processes. To clarify the panpsychistic framework of this paper, the psyche is a characteristic of all existing things, while sensation is peculiar only to living organisms; consciousness is pervasive into the animal kingdom and self-consciousness typical of man and, probably, of some higher animals.
| All Organisms | Animals | Humans | |
|---|---|---|---|
| Psyche/Mind | X | X | X |
| Sensation | X | X | |
| Consciousness | X | ||
| Self-conscious | X |
Here we will not address any solution to the combination problem, nevertheless we will postulate (we will denote this panpsychistic hypothesis as H1) that sensation, consciousness and self-consciousness are different elaborations of the psyche, which must be considered the elementary state from which all the others are derived.
Once we have accepted the possibility that the psyche is a basic category of existing reality, like space, time and energy, it can be fruitful to analyze the properties and relations that connect these categories. Indeed, 20th century physics has studied fundamental relationships linking space, time and energy, showing theoretical constraints between them as in the case of Heisenberg's uncertainty principle. Since, in our framework, the psyche is inherent to matter and since matter is linked to energy through the famous mass-energy equivalence relation, i.e. $E = mc^2$; it is therefore logical to assume (later we will refer to this panpsychistic hypothesis as H2) that psyche must be linked to energy by some form of relation.
In this paper we will proceed in this direction suggesting a quantitative, and theoretically measurable, relation that involves the flow of energy and consciousness by the use of Landauer Principle.
Landauer's Principle
Landauer's principle states that creation and destruction of information requires a minimum amount of energy, which is needed in the creation of information and released in the dispersal process. In other words, creating and erasing information in a system is an irreversible process that should require a minimum amount of work (Jun 2014).
The actual amount of energy needed was identified by Landauer (Landauer 1961) as:
where $k_b$ is the Boltzmann constant, $T$ is the room temperature in kelvins and $\ln(2) b$ represent the quantity of information, here measured in bit.
To understand better the above formula, we need to explain what we intend for information and how this principle is derived. We will follow Shannon axiomatic approach (Shannon 1948) defining the information I, extracted from observing an event, as a real continuous positive function of the probability p of that event to occur or not, i.e. $I(p) \geq 0$. An event that is certain, i.e. $p = 1$, yields to no information on its occurrence, i.e. $I(p) = 0$.
Moreover, Shannon postulated that given n independent events of individual probabilities $p_i$ (therefore with joint probability $p_1 p_2 \cdots p_n$) then the information resulting from observing the set of events would be the sum of the individual event's information, i.e. $I(p_1 p_2 \cdots p_n) = I(p_1) + \cdots + I(p_n)$.
With this premises, Shannon noted that the only function satisfying these axioms was a logarithmic function $H(x)$ which had a close resembles with an information entropy function. He then defined such entropy function using Boltzmann thermodynamic entropy and obtaining:
Which, in the limit of a single bit of information, i.e. $H(x) = 1$, yields to the information entropy of one single bit:
Starting from these considerations, Landauer (Landauer 1961) first proposed a link between thermodynamics and information by postulating that logical irreversibility of a computational process implies physical irreversibility. As a logical consequence of this assumption, it can be easily shown (Vopson 2019) that the process of creating information requires a work $W \geq k_b T \ln(2)$ externally applied to create a bit of information, while the process of erasing a bit of information generates heat energy $Q \geq k_b T \ln(2)$ released to the environment.
Although Landauer's Principle was formulated and established in a specific experimental setting, it was later extended as a general principle in order to solve the paradox posed by Maxwell's demon (Bennett 1982). In recent years the principle has been shown to be valid under much broader conditions, confirming that it may constitute an essential, non-contingent constraint linking information and energy (Bérut 2012; Vopson 2019) not only in the realm of classical physics but also in the quantum realm (Gaudenzi 2018).
What Landauer's Principle says on Consciousness
It is worth noting that while the notion of psyche and that of sensation do not involve any transfer or flow of information, the notion of consciousness and self-consciousness, by their very same definition given above, do. Nevertheless, it is important to stress out that neither consciousness nor self-consciousness are information, but they are related to information since they both involve the reception and re-elaboration of stimuli in an organic and coordinated way in order to acquire information and, therefore, knowledge (from the exterior world or the self, respectively).
Considering energy-information equivalence express by Landauer's Principle as universal, and therefore postulating its validity on all possible realms; assuming the panpsychistic hypothesis H1 and H2 previously stated; then, we might use Landauer's Principle to measure the flow of information and, therefore, the presence of consciousness in an organism.
Indeed, let T be the temperature in which the process is developed and derive equation (1) in respect to time, we then obtain:
which, in case of constant temperature, i.e. $\frac{dT}{dt} = 0$, yields to:
i.e. the flow of information $\frac{db}{dt}$ is directly proportional with a flow of energy. In our framework, this implies that consciousness, which involves a flow of information, would be measurable as flow of energy, i.e. in case of a conscious process we would assist to an apparent violation of the conservation of energy.
Toward an Experimental Set-up
An experimental set-up that can measure an energy violation during a conscious process can be challenging and, in case...