Entropy for a Sovereign Second Law
It's time for a real thermodynamic entropy
Entropy is the foundation of the universe, if the Second Law is sovereign.
Second Law Ontology:
Entropy > Energy > Spacetime > Mass
Traditional Physics:
Spacetime > Energy > Mass > Entropy
If the Second Law is sovereign, then entropy is real and clearly embodies an arrow of time, and is not observer dependent.
There also needs to be an entropy capable of representing order in the universe, and not just an improbabilistic combination of particles.
Here I will go through a few of the most known entropies, (there are at least 10+…) and see that all have flaws which preclude its use from a real thermodynamic entropy of a sovereign Second Law.
Boltzmann Entropy
SB=klnΩ
Counts number of micro-configurations compatible with a single macro state.
Assumes the Second Law is a statistical emergent law, and not sovereign
Is ergodic (explores a fixed phase space)
Order paradox emerges, order clearly appears everywhere in the universe at all scales, but an “ordered state” is observer dependent, and any particular state is improbable.
Measures “disorder” in the system, but “disorder” lacks a rigorous definition
Does not explain higher dimensional orders that appear everywhere in the universe (dissipative structures)
Assumes entropy is just “heat”; no way to unify heat, turbulence, and gravitational entropy under this definition
Good enough for entropy accounting mechanism to understand how heat engines work
Shannon Entropy
H=−∑pilogpi
Measures compressibility, or representability of a system in bits
The cost of describing uncertainty, not the physics generating it
Gets used in “information first” physics theories, i.e. Law of Functional Information
What is order and what is entropy is not apparent
Is epistemic, and descriptive only
Does not require irreversibility
Useless for a sovereign Second Law
Gibbs Entropy
SG=−k∑pilnpi
Measures how much uncertainty is due to your lack of knowledge about the microstate
Used in statistical mechanics
Is reversible
Used to try to represent entropy with geometry
Not compatible with a sovereign Second Law
Entanglement entropy
Entanglement entropy counts the DOF that cannot be assigned to subsystem A or B alone.
Used in black hole thermodynamics
Used in holography entropy theories
Generates geometry in toy AdS universes where the Second Law doesn’t operate
Can’t distinguish between heat, turbulence or gravitational entropy
Can’t serve as real entropy for a sovereign Second Law
Chain Entropy (real thermodynamic irreversible Entropy of evolving phase space dimensionality)
Schain = DOFrealized + DOFlatent
This is the first entropy compatible with a sovereign Second Law
DOFrealized measures energy that has no forbidden states, can couple to all modes, and DOF like a photon
DOFlatent measures energy that has to occupy a smaller phase space due to geometric constraints (fields, gravity, or spacetime itself)
Similar to non-ergodicity, but actual dimensionality of phase space changes
If entropy is real and the Second Law is sovereign, the universe must track latent entropy and ensure its dissipation, which can only be gravity
Energy with no forbidden states, and can couple to all modes travels at c, does not gravitate because energy is not in restricted phase space
Energy with constraints, forced into smaller phase space is latent entropy to some degree. This includes mass, and all order in the universe
Realized entropy (phase space expansion) must be earned through dissipation.
Total Chain Entropy does not increase nor decrease
Key Property: Irreversibility/Non-Invertibility
f:X→Y, ∣Y∣>∣X∣⇒f−1 does not exist
When DOF decohere to produce more DOF, there is no invertible mapping.
Quantum collapse has rearranged the global entanglement super graph.
Allows modeling of turbulence, heat and radiation.
Key Property: Non Unitarity/Information Destroy
DOFlatent or latent entropy, is energy that can not be expressed fully in DOF, that is shoved into a smaller phase space.
A sovereign Second Law must keep a bookkeeping mechanism for this.
When a hot plasma falls into a black hole the universe has lost access to phase space or microstates of possibility.
Gravitational collapses always result in a reduction in phase space.
Latent entropy gives a way to account for lost phase space, compensated by curvature (gravity) which guarantees coupling, and therefore dissipation in the future.
So if mass falls into a black hole, its volume increases relative to lost phase space, which is proportional to volume of the black hole.
Black holes, mass, order and latent entropy gravitate exactly because something has been “irreversibly forgotten”
Resolves black hole information paradox, because information is destroyed, but tracked by gravity
Key Property: Maps onto global entanglement hypergraph
A crude description for DOF of different size
There is no good reason to believe the universe sees entropy as made up of only molecules
Choosing to denominate entropy in molecule microstates is admission that you think entropy is “information” only, observer dependent, limits of description
A hypergraph is a graph where one edge can connect multiple nodes
In this crude drawing, a diamond is a molecular DOF, a pentagon a thermal-ish DOF, and a star a more coherent DOF
This description allows a rough mapping of entropy/DOF onto global entanglement super graph, can describe everything from order, turbulence, heat, radiation, or higher dimensional orders such as Earth climate system
Key Property: Unifies order, heat, turbulence, gravitational entropy, life, and all higher dimensional order into one definition
All modes of energy can be expressed in terms of Chain Entropy
Vacuum/0-point energy is just maximum realized DOF
A black hole below or somewhere below the horizon may sit a singularity, or maximum latent entropy
Mass is very high latent entropy that is stable above the vacuum state. Mass is the combinatorial building block for higher dimensional orders
Maximum latent entropy isn’t mass anymore because there are no distinctions available for constraint anymore
Key Property: Ground State
Chain entropy has a DOFrealized term, which represents energy fully realized as real entropy
Heat is not the end state of entropy, it is dissolution into spacetime/vacuum expansion
Blackhole latent entropy and latent entropy in galaxies may relax their curvature into the vacuum. This could be the broadband nHZ background picked up by LIGO/PTA that GR has no current explanation for
PV mode of a gas would not be a fundamental law, just a relation between potential spread into volume, vs pressure (latent entropy/potential energy that can be coupled to and produce work), activated when matter crosses a temperature threshold
Photons will gradually be redshifted to nothingness, the energy “disappears” into the vacuum
Higher temperature matter has more energy in fewer degrees of freedom, than cold temperature, it is more latent entropy relative to the ground state
This matches Carnot efficiency logic, the same energy activates more DOF at colder temperatures than higher, the remainder of which is max theoretical that can be turned to work
If the same amount of energy at higher temperature is more latent and must gravitate more than the same amount of energy at colder temperature, to keep the Second Law sovereign, then classical General Relativity is making a category error. It treats both energy quantities as equal weight in gravity calculation.