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The kinetic-equation approach to particle production in strong, time-dependent external fields is revisited and three limiting cases are discussed for different field patterns: the Sauter pulse, a harmonic pulse with a Gaussian envelope, and a Poisson-distributed stochastic field. It is shown that for transient subcritical electric fields <inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> a finite residual particle number density <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>(</mo> <mo>&#8734;</mo> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> would be absent if the field-dependence of the dynamical phase in the Schwinger source term would be neglected. In this case the distribution function of created particles follows the law <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"></mspace> <mo>&#8764;</mo> <mspace width="3.33333pt"></mspace> <msup> <mi>E</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>. Two lessons for particle production in heavy-ion collisions are derived from this exercise. First: the shorter the (Sauter-type) pulse, the higher the residual density of produced particles. Second: although the Schwinger process in a string-type field produces a non-thermal particle spectrum, a Poissonian distribution of the (fluctuating) strings produces a thermal spectrum with an apparent temperature that coincides with the Hawking&#8211;Unruh temperature for the mean value of the string tension.