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Equation 18 · Part 7 · The Statistical Mechanics of Irreversibility at Molecular Scale

subscript

ssys(t)=−kBln⁡p(xt,t).s_{\mathrm{sys}}(t) = -k_{\mathrm B}\ln p(x_t,t).
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

The system’s stochastic entropy is defined from the ensemble density evaluated at the realized state, ssys(t)=−kBln⁡p(xt,t)s_{\mathrm{sys}}(t) = -k_{\mathrm B}\ln p(x_t,t). For a single thermal bath, the medium entropy change is related to dissipated heat, subject to sign convention, and total entropy combines system and medium contributions. This allows every observed path to receive a thermodynamic accounting while preserving the distinction between a random trajectory-level quantity and its ensemble expectation [ 4 ] .

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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