Time Series Entropy Calculator

Measure disorder in signals with practical entropy tools. Compare Shannon, sample, approximate, and permutation methods. Use exports to document physics results with confidence today.

Calculator

Example Data Table

Case Series Suggested method Reason
Sensor noise 1.02, 1.09, 0.98, 1.15, 1.21 Shannon entropy Checks spread across amplitude bins.
Vibration pattern 3, 4, 3, 5, 4, 6, 5 Sample entropy Tests repeated embedded shapes.
Chaotic signal 2.1, 3.8, 1.4, 4.2, 2.9 Permutation entropy Studies ordinal ordering.

Formula Used

Shannon Entropy

H = - Σ pi logb(pi)

Here, pi is the probability of bin i. The base b controls the unit. Base 2 gives bits.

Normalized Shannon Entropy

Hnorm = H / logb(k)

Here, k is the selected bin count. Values near one show broad state use.

Entropy Rate

H(Xt | Xt-1) = H(Xt-1, Xt) - H(Xt-1)

This estimates new information after the previous binned state is known.

Approximate Entropy

ApEn(m,r) = φm(r) - φm+1(r)

It compares repeated embedded patterns with dimension m and tolerance r.

Sample Entropy

SampEn(m,r) = -logb(A / B)

B counts matching patterns of length m. A counts matching patterns of length m + 1.

Permutation Entropy

Hperm = - Σ p(π) logb(p(π))

Here, π represents an ordinal pattern from each embedded window.

How to Use This Calculator

  1. Paste numeric time series values into the input box.
  2. Select the delimiter, or keep auto detect.
  3. Choose one entropy method, or run all methods.
  4. Set bins for Shannon entropy and entropy rate.
  5. Set dimension, delay, and tolerance for pattern methods.
  6. Choose preprocessing only when it matches your analysis goal.
  7. Press the calculate button to view the result above the form.
  8. Use CSV or PDF export for reports and records.

Entropy in Physics Signals

Entropy helps describe disorder in a measured signal. A quiet and repeated series has low entropy. A changing series has higher entropy. In physics, this idea helps compare noise, turbulence, vibration, heat records, and sensor output. The value does not prove randomness alone. It gives a compact measure of spread, pattern variety, and predictability.

What This Tool Measures

This calculator accepts a numeric time series. It then prepares the values and applies selected entropy methods. Shannon entropy studies the distribution of binned values. Entropy rate estimates how much new information appears after the previous state. Approximate entropy checks repeated shapes. Sample entropy checks similar patterns while avoiding self matches. Permutation entropy studies ordinal order, so it is useful when amplitude scale changes.

Choosing the Method

Use Shannon entropy when the main question concerns amplitude states. Use entropy rate when sequence order matters. Use approximate entropy for short records that may contain repeated behavior. Use sample entropy for cleaner records and stronger pattern testing. Use permutation entropy for chaotic, nonlinear, or noisy signals. The all methods option gives a broad review.

Input Quality Matters

Entropy depends on sampling, scaling, and preprocessing. Remove clear recording errors first. Use equal width bins for physical ranges. Use equal frequency bins when values cluster heavily. Keep the bin count reasonable. Too many bins can create false disorder. Too few bins can hide real structure.

Tolerance and Embedding

Approximate and sample entropy need an embedding dimension. A common starting value is two. They also need tolerance. A common starting value is 0.2 times the standard deviation. Larger tolerance finds more matches. Smaller tolerance demands closer patterns. Delay controls spacing between points in each pattern.

Reading the Result

A higher entropy value usually means greater complexity. A normalized value near one means many states are used evenly. A value near zero means repeated or concentrated behavior. Compare signals only when settings match. This keeps the interpretation fair.

Practical Physics Use

You can compare two trials with the same setup. You can test filtering effects. You can also check whether a process becomes more stable over time. Always save the settings with each result. Small choices can change the final entropy value and trends.

FAQs

What is time series entropy?

It is a numerical measure of disorder, uncertainty, or pattern complexity in ordered data. Higher values often mean less predictable behavior.

Which method should I choose first?

Start with Shannon entropy for amplitude spread. Use sample or permutation entropy when sequence patterns matter more than simple value distribution.

What does normalized entropy mean?

Normalized entropy scales the result against a maximum possible value. It helps compare results across similar settings.

Why do bins affect Shannon entropy?

Bins define the states used for probability estimates. Too few bins hide variation. Too many bins can exaggerate disorder.

What is tolerance in sample entropy?

Tolerance sets how close two embedded patterns must be to count as matching. A common start is 0.2 times standard deviation.

What is embedding dimension?

Embedding dimension is the number of points used in each pattern window. Larger values need longer data records.

Can I use unevenly sampled data?

The calculator accepts values only. For physical timing accuracy, resample uneven data before entropy analysis.

Why is sample entropy infinite?

It can happen when shorter patterns match, but longer patterns do not. More data or a larger tolerance may help.


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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.