In the collection Physics and computation
How are entropy, information and the arrow of time linked?
Entropy counts possible arrangements of a system and is tied to missing information. Its tendency to rise is the usual basis for time's direction, though the details remain actively studied.
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The short answer
Entropy measures how many arrangements a system can be in, and information theory treats that same quantity as a measure of how much is unknown about the system. The arrow of time is the observed one-way direction of change, which is conventionally identified with the rise of entropy. Researchers now treat these three ideas as closely related, and several current papers explore how far information can be used to define or refine the arrow of time. [1] [2]
Entropy as counting arrangements
In precise terms, entropy is a measure of the number of possible arrangements a system of particles can be in. These possibilities grow when energy is spread more evenly among more particles, which is why entropy rises as energy disperses. In 1948 Claude Shannon, founder of information theory, showed that entropy also tracks inversely with information: the less you know about a data set, the more states it could be in, and so the higher its entropy. [1]
A 2016 paper by Spinney, Lizier and Prokopenko notes that many concepts and quantities in thermodynamics and information theory are shared, and asks whether information is physical. The Journal of Physical Chemistry B article on the topic likewise sets out to investigate the relationship between thermodynamic entropy and information theory and what it implies for the arrow of time. [2] [3]
Entropy and the direction of time
Everyday examples show the thermodynamic arrow: smoke billows from chimneys and does not flow back in, and a plate that smashes on the floor does not reassemble. The flow of time is considered synonymous with this arrow, in which entropy increases and does not decrease. For small systems, recent work has formalized that this law holds only statistically. In equilibrium, where there is no entropy production, no test can tell whether time is running forwards or backwards. [2]
The Information Philosopher site adds a cosmological point: without expansion, a static closed universe would settle into thermal equilibrium, and expansion leaves room for order or information to increase even while entropy increases. [4]
Where information changes the picture
Spinney and colleagues argue that when a system involves feedback, or an observer looks at only part of it, the usual statistical form of the second law need not hold, and an observer could be systematically misled about which way time flows. They propose adding an information-theoretic term, built from mutual information and transfer entropy, to the usual entropy production. They argue that the combined physical and informational arrow of time holds in all circumstances, while each component alone can run either way. This is one group's proposal, not a settled consensus. [2]
Other work links information to time's direction through memory and agents. One arXiv paper discusses how the formation of memory and the use of agency draw on information stored in low entropy. Another argues that algorithmic entropy takes conceptual precedence over other entropy notions and relates it to scientific induction and the psychological arrow of time. Physicist Huber, quoted in Quanta, suggests that limits on a clock's entropy production should correspond to limits on information about the time that has passed. [5] [6] [1]
Sources
- The New Science of Clocks Prompts Questions About the Nature of Time | Quanta Magazine (quantamagazine.org) Found by source search. Not checked by a person.
- Transfer entropy in physical systems and the arrow of time (lizier.me) Found by source search. Not checked by a person.
- Entropy, Information, and the Arrow of Time | The Journal of Physical Chemistry B | ACS Publications (pubs.acs.org) Found by source search. Not checked by a person.
- The Arrow of Time (informationphilosopher.com) Found by source search. Not checked by a person.
- arxiv.org (arxiv.org) Found by source search. Not checked by a person.
- Information dynamics and the arrow of time (arxiv.org) Found by source search. Not checked by a person.
Questions to follow next
- Why did the universe start with low entropy?
- What is transfer entropy and how is it measured?
- Can a clock measure time without increasing entropy?