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Equation 18 · Part 2 · The Statistical Mechanics of Irreversibility at Molecular Scale

Symbol t

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

What this part means

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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