Physical systems have particles with properties, locations, times, motions, energies, momenta, and relations. Particles can be independent or depend on each other.
degrees of freedom
Related particles have motion restrictions. Particles with no relations are free to move in all directions by translations, vibrations, and rotations. Systems have interchangeable states {degrees of freedom, entropy}. More particles and more particle independence increase degrees of freedom.
order
Order depends on direction constraints. Ordered systems have few possible states. Disordered systems have many possible states. Systems with high heat have more disorder because kinetic energy goes in random directions and potential energy decreases. Systems with work have less disorder because kinetic energy goes in one direction and potential energy increases in direction against field. Systems have disorder amount {entropy, heat}|.
information
Systems with no relations have no information, because particles move freely and randomly, with no dependencies. Systems with relations have information about relations and dependencies. Systems with more degrees of freedom, less order, and more entropy have less information. Systems with fewer degrees of freedom, more order, and less entropy have more information. Because entropy relates to disorder, entropy relates to negative information.
information: amount
The smallest information amount (bit) specifies binary choice: marked or unmarked, yes or no, 0 or 1, or on or off. The smallest system has two possible independent states and one binary choice: 2^1 = 2, where 2 is number of states and 1 is number of choices. Choices can always reduce to binary choices, so base can always be two. Systems have number of binary choices, which is bit number.
information: probability
The smallest system is in one state or the other, and both states are equally probable, so states have probability one-half: 1/2 = 1 / 2^1. State probability is independent-state-number inverse.
information: states
Systems have independent states and dependent states. Dependent states are part of independent states. Systems can only be in one independent state. Particles have free movement, so independent states can interchange freely and are equally probable. Particles have number {degrees of freedom, particle} of independent states available. Systems have number of states. Number is two raised to power. For example, systems can have 2^6 = 64 states. States have probability 1/64 = 1 / 2^6. 6 is number of system information bits. Systems with more states have more bits and lower-probability states.
information: degeneracy
Different degenerate states can have same properties. For example, systems with two particles can have particle energies 0 and 2, 2 and 0, or 1 and 1, all with same total energy.
information: reversibility
Particle physical processes are reversible in time and space. Physical system states can go to other system states, with enough time.
entropy: probability
Disorder depends on information, so entropy depends on information. Entropy is negative base-2 logarithm of probability. For example, for two states, S = -log(1 / 2^1) = +1. For 64 states, S = -log(1 / 2^6), so S = -log(1 / 2^6) = +6. More states make each state less likely, so disorder and entropy increase.
entropy: degeneracy probability
Degenerate-state groups have different probabilities, because groups have different numbers of degenerate states. Groups with more members have higher probability because independent states have equal probability. Entropy depends degeneracy pattern. Going to lower probability group increases system order and has less entropy. Going to higher probability group decreases system order and has more entropy.
Lowest-probability groups are reachable from only one other state. High-probability groups are reachable from most other states. Systems are likely to go to higher-probability groups. Systems move toward highest-probability group. In isolated closed systems, highest-probability group has probability much higher than other groups. If system goes to lower-probability group, it almost instantly goes to higher-probability group, before people can observe entropy decrease. Therefore, entropy tends to increase.
entropy: additive
Entropy and disorder are additive, because they depend on independent states, degrees of freedom. Systems with independent parts have entropy equal to sum of part entropies. If parts are dependent, entropy is less, because number of different states is less.
entropy: heat
Heat is total random translational kinetic energy. Temperature is average random translational kinetic energy. Entropy S is heat energy Q, unavailable to do work, divided by temperature T: S = number of independent particle states = (total random translational kinetic energy) / (average random translational kinetic energy) = Q/T. Kinetic energy is random, and potential energy holds molecules apart in all directions, so heat has no net direction. Average direction is zero.
entropy: energy
At constant pressure and temperature, entropy is enthalpy change divided by temperature, because heat is enthalpy change at constant pressure and temperature. At constant volume and temperature, entropy is energy change divided by temperature, because heat is energy change at constant volume and temperature.
entropy: gravity
If no gravity, entropy increases as particles spread, because particle occupied volume increases. If gravity, entropy increases as particles decrease separation, because potential energy becomes heat though particle occupied volume decreases. If antigravity, entropy increases as particles increase separation, because potential energy becomes heat and particle occupied volume increases.
entropy: mass
Entropy increases when particle number increases. Matter increase makes more entropy. Entropy increases when particles distribute more evenly, toward thermal equilibrium, and have fewer patterns, lines, edges, angles, shapes, and groupings.
entropy: volume
If there are no forces, volume increase makes more possible molecule distributions, less order, and more entropy. If there are forces, volume decrease makes more possible molecule distributions, less order, and more entropy. See Figure 1.
entropy: directions
Energy dispersal increases entropy, because disorder increases. Increasing number of directions or motion types increases entropy. Mixing makes more disorder and more entropy. More randomness makes more entropy. More asymmetry makes more disorder and more entropy.
entropy: heat
Work makes more friction and heat and more entropy. Making heat makes more randomness and more entropy.
entropy: fields
Field strength decrease disperses energy and makes more entropy.
entropy: force and pressure
Pressure decrease disperses energy and makes more entropy. Force decrease disperses energy and makes more entropy.
entropy: volume
At phase changes, pressure change dP divided by temperature change dT equals entropy change dS divided by volume change dV, because energy changes must be equal at equilibrium: dP / dT = dS / dV, so dP * dV = dT * dS. Volume increase greatly increases entropy.
entropy: increase
Systems increase entropy when disorder, degrees of freedom, and disinformation increase. Information decrease makes more interactions and more entropy. Order decrease, as in state change from liquid to gas, increases entropy.
entropy: decrease
Many factors increase order, regularity, or information, such as more regular space or time intervals, as in stripes and waves. Higher energy concentration, more mass, larger size, higher density, more interactions, more relations, smaller distances, closer interactions, more equilibrium, more steady state, more interaction templates, more directed energy, and more filtering increase order.
More reference point changes, more efficient coding or language, better categorization or classification, more repetition, more shape regularity, and more self-similarity at different distance or time scales increase order. More recursion, bigger algorithms, more processes, more geodesic paths, more simplicity, lower mixing, and more purity increase order. More reconfigurations, more object exchanges, and more combining systems increase order. Fewer functions, fewer behaviors, more resonance, fewer observations, more symmetry, more coordinated motion, and more process coupling increase order.
Larger increase in potential energy increases order, because energy concentrates. Higher increase in fields increases order, because energy increases. Fewer motion degrees of freedom, as in slow and large objects, increase order. More same-type, same-range, and same-size interactions increase order. More and equal influence spheres increase order. Higher space-time curvature increases order. More constant space-time curvature increases order.
Lower harmonics of Fourier series increase order. Fewer elements in Fourier series increase order.
entropy: closed system
In closed systems, entropy tends to increase, because energy becomes more random. Potential energy becomes random kinetic energy by friction or forced motion. Random kinetic energy cannot all go back to potential energy because potential energy has direction. Work kinetic energy becomes random kinetic energy by friction or forced motion. Random kinetic energy cannot all go back to work energy because work energy has direction. Heat energy is already random. Only part, in a direction, can become potential energy or work kinetic energy. Radiation becomes random kinetic energy by collision. Random kinetic energy cannot all go back to radiation energy, because radiation energy requires particles accelerated in direction.
universe entropy
Universe is isolated closed system. It started in low-entropy state and moves to higher entropy states.
Perhaps, at beginning {hot big bang} {primordial fireball}, universe had one particle at one point with smallest possible volume, and so no relations among parts. There were no space fields and no tidal effects. Universe had highly concentrated energy at high temperature and so large contracting forces and high pressure. Particle number remained the same or increased, as particles and radiation split.
Universe expansion increased space volume. Space points became farther from other points. Expansion was greatest at first. Then expansion slowed, because all particles had gravity.
As universe cooled, it created particles, in evenly distributed gas. Entropy increased but was still low.
As universe cooled, gas-particle gravity formed galaxies and stars. Condensed gas had higher entropy but was still low. Potential energy converted to heat as infalling particles collided. Heat and mass concentrated in stars.
Stars are hot compared to space, so stars can transfer energy to planets and organisms. Stars undergoing nuclear fusion make visible light. Visible light has higher energy than heat infrared radiation. On Earth, temperature stays approximately constant. Therefore, visible light energy that impinges on Earth is equal to energy that radiates away from Earth as heat. Because sunlight has higher energy per photon, fewer sunlight photons land on Earth than Earth emits as infrared heat photons. Entropy increases in space, and total universe entropy increases. On Earth, order increases and disorder decreases, mostly in organisms. From universe beginning until now, universe entropy increases, while small-region physical forces and particle motions can cause entropy decreases.
Now, universe has many photons, large volume, negligible forces, and even matter distribution, so universe entropy is now large. For example, cosmic microwave background radiation has many randomly moving photons, from soon after universe origin. Photons mostly evenly distribute. They fill whole universe and have little effect on each other. As universe expands, their entropy becomes more.
Now, universe has many galaxies with central black holes and has black holes formed after supernovae. Black holes are mass concentrations denser than atomic nuclei. Black holes have very high entropy, because particle number is high, volume is small, mass evenly distributes, gravitational force and fields are high, and density is high. Black holes make universe entropy large now.
In the future, universe entropy will increase. Universe will have more black holes and can evolve to have only black holes. Universe will have more local forces. Universe will have more volume. Universe will have more particles. Universe will have more-even particle distribution.
Systems have particles, which have position and momentum, and energy and time {information, physics}.
spin system
Particles can have spin up clockwise or spin down counterclockwise. Particle spin state encodes one binary choice or information bit: 0 or 1. For quanta, such as spin, state holds one quantum information bit. One kilogram of plasma in one liter of space can hold 10^31 bits.
Particles with known spins can carry input or output information. For interacting particles, quanta can entangle, and information can entangle. Particles can interact to represent computation to calculate. Bits can change electromagnetically every 10^-20 second. Signals travel 3 * 10^-12 seconds to next particle. System particles entangle and change in parallel. One kilogram of plasma in one liter of space can have 10^51 particle-spin changes each second.
system information
Information required to describe system state depends on degrees of freedom. Mole of chemical has 10^23 degrees of freedom because it has that many molecules. In regions that have no boundary and have uniform matter and energy, entropy is proportional to volume.
black hole
By Bekenstein-Hawking formula, one-kilogram black holes have radius 10^-27 meters. Event-horizon surface can hold 10^16 bits. Bits can change every 10^-35 second. Surface can have 10^51 particle-state changes each second. Light can cross black holes in 10^-35 seconds, so physical processes have time to work serially.
Observers cannot see past event horizon, so horizon surface must contain all information about region volume inside black hole. Gravity causes information bits to interact, so entanglement over surface area can have enough information states to hold information about inside volume. Black-hole entropy is directly proportional to event-horizon surface area. Planck area is 10^-66 cm^2. One Planck area has 0.25 information bit, so four Planck areas make one bit.
One-kilogram black holes emit gamma and higher-energy rays by Hawking radiation and disappear in 10^-21 second. Smaller black holes dissipate faster and emit higher energies.
Perhaps, rather than particle spins and states, branes or strings hold states.
cell size
Bit-change maximum rate is maximum clock frequency, and so time has quanta. Rate depends on gravitational constant, light speed, and Planck constant.
Space has quanta, with cell sizes. Black holes have maximum energy per volume and have definite ratio between mass and event-horizon radius, so maximum mass-energy is proportional to space-time radius. Cell size varies with radius cube root. For universe, cell diameter is 10^-15 meters.
Energy and time relate, so space cell size depends on space-time radius. The holographic principle can derive from uncertainty principle.
universe
Universe has age 1.3 * 10^10 years and so radius 1.3 * 10^10 light-years. Universe is close to maximum density, so it can hold 10^123 bits. It can have 10^106 bit changes each second, in parallel, from 10^72 joules. It has 10^92 bits of ordinary matter, which can change bits at 10^14 Hz. It has less than 10^123 bits of dark energy, which can change bits at 10^18 Hz.
Total entropy in universe, inside and outside black holes, cannot go down {generalized second law} (GSL).
Information that went into black hole can come out by entanglement of two surface virtual particles, one of which interacts with original matter and information at singularity {Horowitz-Maldacena model}.
Information bits can change no faster than quantum time. Heisenberg uncertainty principle relates energy and time. Quantum time t depends on quantum energy E {Margolus-Levitin theorem}: t >= h / (4*E), where h = Planck's constant.
Masses in volumes can hold limited entropy amounts {universal entropy bound}.
Energy and mass within volume can hold limited entropy amount {holographic bound}. Holographic bound is number of event-horizon-surface Plank areas divided by four. Maximum-entropy regions relate mass and volume, so area can define region information. Black-hole formation prevents volume entropy increases from overtaking surface entropy increases and so limits entropy.
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Date Modified: 2022.0225