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Equation 18 · Part 5 · The Statistical Mechanics of Irreversibility at Molecular Scale

Symbol x_t

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

What this part means

xtx_t is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

xtx_t is one of the signed contributions combined to compute the quantity on the left.

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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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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