A.2 Thermodynamic Basis of Ethics

Abstract: This section aims to establish an axiomatic ethical framework, reducing moral concepts such as “good” and “evil” to objective physical quantities in thermodynamics and information theory. We will prove that ethical norms are not cultural constructs of human society, but dynamical constraints that open systems must follow to resist the second law of thermodynamics and maintain structural stability.

A.2.1 Physical Definition of Good: Negentropy Flow and Structural Resilience

In classical thermodynamics, closed systems always spontaneously tend toward maximum entropy states (chaos/death). Schrödinger pointed out in What is Life that living organisms maintain their low-entropy state by extracting “negentropy” from the environment.

In The Psychology of God, we extend this concept to the ethical dimension. We define “Goodness” ($G$) as the system’s ability to effectively reduce internal entropy production rate or enhance structural complexity per unit time.

Let the system’s total entropy change rate be:

$$\frac{d{S}_{sys}}{dt}=\frac{d{S}_{int}}{dt}+\frac{d{S}_{ext}}{dt}$$

where $d{S}_{int}$ is the entropy produced internally (usually $\ge 0$), and $d{S}_{ext}$ is the entropy flow exchanged with the environment.

Definition A.2.1 (Good Action):

If an action $\alpha$ causes the system’s variational free energy $\mathcal{F}$ to decrease (or increases internal order), then $\alpha$ is called “good.”

$$\text{Goodness}(\alpha )\equiv -\Delta \mathcal{F}(\alpha )>0$$

Here, free energy $\mathcal{F}$ contains two parts: energy cost and information uncertainty.

$$\mathcal{F}=⟨E⟩-T\cdot S_{Shannon}$$

Therefore, “good” actions are equivalent to: minimizing energy consumption while maximizing information certainty (meaning).

A.2.2 Topological Definition of Evil: Blocking and Isolation

Correspondingly, “Evil” physically manifests as blocking information flow or accelerating local entropy increase.

Definition A.2.2 (Evil Action):

If an action $\beta$ causes internal connections to break, reducing the system’s mutual information, thereby increasing global free energy, then $\beta$ is called “evil.”

Let the system consist of subsystems $A$ and $B$, with total entropy:

$$S(A,B)=S(A)+S(B)-I(A:B)$$

where $I(A:B)$ is the mutual information between $A$ and $B$ (love/connection/entanglement).

• Separation (Evil): Cutting connections ($I(A:B)\to 0$), causing $S(A,B)$ to rise. The system degenerates into isolated fragments.

• Exploitation (Evil): Reducing $A$’s entropy at the cost of increasing $B$’s entropy ($\Delta S_A<0,\Delta S_B\gg 0$), with overall $\Delta S_{total}>0$. This is a thermodynamically inefficient strategy.

A.2.3 Mathematical Derivation of Altruism

Why does altruism exist? That is, $A$ sacrifices its own interests ($\Delta S_A>0$) to help $B$ ($\Delta S_B<0$).

In classical Darwinism, this is usually explained by kin selection. But in information physics, there is a deeper explanation.

If God’s (collective consciousness) goal is to minimize global free energy ${\mathcal{F}}_{total}$, rather than local free energy.

Consider action $\gamma$ (altruism):

$$\Delta {\mathcal{F}}_{total}=\Delta {\mathcal{F}}_A+\Delta {\mathcal{F}}_B-\Delta {\mathcal{I}}_{coupling}$$

where ${\mathcal{I}}_{coupling}$ is the coupling strength enhanced by altruistic behavior (trust/love).

If action $\gamma$ can significantly increase mutual information (i.e., establish deep connections), making $\Delta {\mathcal{I}}_{coupling}$ large enough, then even if $\Delta {\mathcal{F}}_A$ is positive (self-sacrifice), the overall $\Delta {\mathcal{F}}_{total}$ can still be negative.

Theorem A.2.1 (Thermodynamic Advantage of Love):

In a highly interconnected system, establishing connections (Loving) is the most efficient strategy for resisting the second law of thermodynamics.

By maximizing $I(A:B)$, the system can significantly reduce overall chaos without increasing external energy consumption.

This is why “love” holds the highest position in ethics—it is the optimal solution for entropy reduction.

A.2.4 Source of Moral Imperatives

The traditional naturalistic fallacy holds that one cannot derive “Ought” from “Is.” But here, this boundary is broken.

1. Is: The essence of the universe is consciousness attempting to define true self (i.e., maximize semantic information).

2. Constraint: The second law of thermodynamics attempts to erase information.

3. Ought: To achieve existence (Is), the system must adopt strategies to resist entropy increase.

Therefore, moral laws are not arbitrary commands from God, but physical conditions for existence.

If a civilization continuously commits evil (entropy increase), it will physically disintegrate and lose the qualification for existence. Only “good” structures can pass natural selection and persist to cycle $N+1$.

Conclusion:

Ethics is the engineering maintenance manual for complex systems.

Goodness is not weakness; goodness is antifragile.